
Copyrights? 



COPYRIGHT DEPOSIT; 



TWENTIETH CENTURY TEXT-BOOKS 

EDITED BY 

A. F. NIGHTINGALE, Ph.D. 

SUPERINTENDENT OF HIGH SCHOOLS, CHICAGO 




SIE ISAAC NEWTON (1642-1727). 

Greatest of natural philosophers ; author of Principia ; president of Royal 
Society twenty five years : member French Academy of Sciences ; knighted 1705. 
Buried in Westminster Abbey. 



TWENTIETH CENTURY TEXT-BOOKS 



ELEMENTS OF PHYSICS 



BY 

C. HANFORD HENDERSON, Ph.D. 

PRINCIPAL PRATT HIGH SCHOOL, BROOKLYN 
AND 

JOHN F. WOODHULL, Ph D. 

PROFESSOR OF PHYSICAL SCIENCE, TEACHERS' COLLEGE, 
COLUMBIA UNIVERSITY, NEW YORK 




NEW YORK 
D. APPLETON AND COMPANY 

IQOO 



CHhT 



47696 QJ 



Library of Congress 

Two Copies Received 
SEP 15 1900 

FKSTCOPY. 

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Copyright, 1900 
By D. APPLETON AND COMPANY 



PREFACE 



The authors have prepared this book in the belief that 
physics' should be so taught as to be a desirable and even 
essential subject for every pupil in the secondary schools. 
In its preparation they have therefore devoted much study 
to the conditions which obtain in the schools at the pres- 
ent time, and have endeavored to meet them. 

The book is designed to provide a year's work for the 
class room, and only such matter has been introduced as 
is deemed appropriate for pupils of the high-school age 
and attainments. Laboratory exercises, questions, and 
problems given in a text-book are manifestly inadequate 
and unsatisfactory. The authors have therefore thought 
it preferable not to follow that course, but to amplify and 
make more thorough this part of the study in a separate 
volume, which is published under the title Physical Ex- 
periments, and is to be used concurrently with the text- 
book. 

The relations of physics on all sides to human life and 
human interests have been emphasized. A text-book is 
much more readable if the material for the laboratory work 
is excluded from it. The text-book comprises the infor- 
mational part of the subject, and the authors in this vol- 



VI 



PHYSICS 



ume have imparted to it much warmth and interest. The 
laboratory, on the other hand, deals with inductions and 
verifications, and its chief purpose is to make knowledge 
real. Both the laboratory and the class-room work are 
essential to a correct knowledge of elementary physics, 
and they should correlate in such a manner as to make 
the acquisition of that knowledge interesting as well as 
thorough. The work has been prepared with these essen- 
tials in view. 

In the text-book the subject has been further , human- 
ized by the introduction of a few portraits, with brief 
sketches of the men who, by their researches, have con- 
tributed much to our knowledge of physics. 

A further merit of the work is that the volume is com- 
pact. The subject-matter has been so disposed as to be 
most convenient for class exercises and for the arrange- 
ment of a study plan. A supplement in pamphlet form, 
containing helpful suggestions to teachers using the book 
for the first time, has been prepared, and will be furnished 
without charge. C. H. H. 

J. F. W. 

August, 1900. 



PROPERTIES OF MATTER AND 
MECHANICS OF SOLIDS 

CHAPTER I.— The Content of Physics 

1. The Two Elements in Physical Science. 

2. Matter. 

3. Three States of Matter. 

4. The Three States Continuous. 

5. Radiant Matter. 

6. Motion. 

7. Mass Motion and Molecular Motion. 

8. Force. 

9. Energy. 

10. Matter and Motion. 

11. Physics. 

12. Metaphysics. 

13. The Eternal " Why." 

CHAPTER II.— The Constitution of Matter 

14. The Province of Physics. 

15. Simple and Compound Bodies. 

16. Atoms and Molecules. 

17. Size of Molecules. 

18. Mechanical Mixtures and Chemical Compounds. Fig. 1. 

19. Physical and Chemical Changes. Fig. 2. 

20. Protyle. 

21. Doubt. 

22. The Firm Ground in Physics. 

23. Table of Elements. 

CHAPTER III.— Properties of Matter 

24. Secondary Properties of Matter. 

25. Hardness. 

26. Crystalline Form. 



viii PHYSICS 

27. Cohesion. Fig. 3. 

28. Adhesion. 

29. Elasticity. 

30. Malleability 

31. Ductility. 

32. Viscosity and Brittleness. 

33. Divisibility. Figs. 4, 5, and 6. 

34. Capillarity. Figs. 7 and 8. 

CHAPTER IV.— On Measurement 

35. Science. 

36. Units. 

37. Length. Fig. 9. 



39. Time. 

40. The C.-G.-S. System. 

41. The Two Terms in Measurement. 

42. Methods of Measurement. 

43. Mathematical Physics. 

44. Conservation of Matter. 

45. Conservation of Energy. 

46. Rationality. 

CHAPTER V.— Measurement of Matter 

47. The Problem. 

48. Extension in One Direction. Figs. 10, 11, 12, 13, and 14. 

49. Surveying. 

50. Extension in Two Directions. 

51. Extension in Three Directions. Fig. 15. 

CHAPTER VI.— Mass and Weight 

52. Mass. 

53. Gravitation. 

54. The Formula of Gravitation. 

55. Weight. 

56. Weight as the Measure of Gravitation. 

57. Measurement of Mass. 

58. Weighing. Fig. 16. 

CHAPTER VII.— Density and Specific Gravity 

59. Density. 

60. Specific Gravity. 

61. Specific-Gravity Bottle. Fig. 17. 



PROPERTIES OF MATTER i x 

CHAPTER VIII.— Measurement of Motion 

62. Motion. 

63. Velocity. 

64. Momentum. 

65. Xature of the Motion. 

^6. Path of a Moving Body. Figs. 18 and 19. 

67. Units of Motion. 

CHAPTER IX.— Falling Bodies 

68. Gravitation. 

69. The Value of g. 

70. Falling Bodies. 

71. Projectiles. Fig. 20. 

72. Suggestion. 

73. Vertical Projectiles. 

CHAPTER X.— The Pendulum 

74. Importance of the Pendulum. 

75. The Simple Pendulum. Fig. 21. 

76. The Motion of the Pendulum. Fig. 22. 

77. Formula of the Pendulum. 

78. Discussion of Formula. 

79. Time-keeping and the Seconds Pendulum. 

80. Determination of g by the Pendulum. 

81. The Compound Pendulum. 

CHAPTER XI. — Composition and Resolution of Motions 

82. Composition of Motions. Fig. 23. 

83. Parallelogram of Motions. 

84. Moments. Fig. 24. 

85. Parallel Motions. Figs. 25, 26, and 27. 

86. Resolution of Motions. Fig. 28. 

CHAPTER XII.— Work, Power, and Energy 

87. Work. 

88. Measure of Work. 

89. Power. 

90. Energy. 

91. Forms of Energy. 

92. Transfer and Transformation of Energy. 

93. Xewton's Laws. 

94. Energy — Kinetic and Potential. 



x PHYSICS 

CHAPTER XIII.— Machines 

95. A Machine. 

96. Axiom. 

97. The Principle of Virtual Velocities. 

98. Simple Machines. 

99. The Lever. Figs. 29, 30, 31, 32, 33, and 34. 

100. The Wheel and Axle. Fig. 35. 

101. The Pulley. Figs. 36, 37, 38, and 39. 

102. The Inclined Plane. Figs. 40 and 41. 

103. The Screw. Fig. 42. 

Tables of Contents will also be found on the following pages : 

Mechanics of Fluids, 87, 88. 

Heat, 143, 144. 

Magnetism and Electricity, 207, 208. 

Light, 287, 288. 

Sound, 347. 



PHYSICS: THE SCIENCE OP ENERGY 



CHAPTER I 

THE CONTENT OF PHYSICS 

1. The Two Elements in Physical Science. — Let us call 
up before us a series of occurrences in the outer world : 

An express train dashes past us. A waterfall plunges 
over a precipice. A breath of wind blows against our faces. 
A bird sings in the branch above us. A tree falls in the 
forest. A boy throws a ball. A child picks a flower. 

These several events are apparently very unlike. They 
seem at first sight to have nothing in common ; but when 
we look closer and reduce them to their simplest possible 
terms, we see that they are in reality very much alike. Each 
event contains the same two elements, matter and motion, 
and, from a physical point of view, that is all. Back of the 
matter and motion there may be motive and purpose, but 
we can only infer these. Our senses make direct report 
only of matter and motion. There are different sorts of 
matter and different degrees of motion, but the whole event 
in each case shows only these as the final outer content. 

The study of natural events is therefore the study of 
matter and motion, and must start out with clear general 
ideas concerning these two elements. 

2. Matter may be defined for the present as that which 
occupies space. It naturally prevents anything else from 
occupying the same space. Hence, the essential properties 

2 1 



2 PHYSICS 

of matter, or those properties without which we can not 
conceive matter to exist, are extension and impenetrability. 
Matter makes itself known to us by the testimony of the 
senses. We see it, hear it, smell it, taste it, touch it. But 
observe that, after all, this is indirect testimony. These 
impressions are all of them simply brain impressions. We 
see, hear, smell, taste, touch, in our consciousness .only. We 
can not assert, therefore, that matter exists apart from this 
consciousness. Science has nothing to say about the ulti- 
mate nature of matter. Science studies matter simply as a 
fact of human experience. 

3. Three States of Matter. — Matter manifests itself in 
three states — as solid, liquid, and gas. These states of mat- 
ter, as well as many of its motions, are best explained by 
assuming that matter is made up of extremely small par- 
ticles, or units, which are called molecules. We shall study 
these later somewhat more in detail. 

Solids, at the same temperature, have nearly constant 
volume and approximately constant form. Their molecules 
are so bound together that they can not change their rela- 
tive positions except within very small limits. 

Liquids, at the same temperature, also have nearly con- 
stant volume, but take at once the form of the vessels which 
contain them. Their molecules are free to move among 
themselves, but are not free to fly apart. 

Gases have neither constant volume nor constant form. 
In consequence of the perfect mobility of their molecules, 
they will occupy any space into which they may be intro- 
duced, whatever its volume or form. 

Liquids and gases, on account of the freedom of mo- 
tion possessed by their molecules, are classed together as 
fluids. 

4. The Three States Continuous. — It must not be thought 
for a moment that matter is sharply divisible into solids, 
liquids, and gases. On the contrary, these are only names 
for typical forms of matter. Within the same state we find 



THE CONTENT OF PHYSICS 3 

wide variations from the type, and even between the three 
states themselves we can set np no hard-and-fast lines. 

5. Radiant Matter. — It has been thought that matter 
may exist in still a fourth state, and for this the name 
radiant matter has been proposed. It represents extreme 
dilution and mobility, and bears somewhat the same rela- 
tion to gases that gases do to liquids. We shall study it 
later, when we come to consider Crooke's tubes. 

6. Motion is change of position — a simple definition, but 
one which involves nearly the whole drama of Nature. 

The absence of motion is rest. 

We can only know whether a particle is in motion or at 
rest by comparing it with some other particle whose condi- 
tion is known. But this in turn can only be known by a 
comparison with a third particle, and so on indefinitely. In 
the absence of any fixed reference point in the whole uni- 
verse, we can only know relative motion and relative rest. 

7. Mass Motion and Molecular Motion. — The motion of a 
body may be either of the whole, giving us mass motion ; or 
it may be of the parts, giving us molecular motion. 

When the motion is of the whole, and not too rapid, as 
when an apple falls to the ground or a ball is thrown through 
the air, we can directly watch the change of position. When 
the motion is too rapid for that, as in the passage of a can- 
non ball, we can still observe indirectly the change of posi- 
tion by observing the body first in one place and then in 
another. 

If the motion is confined to the parts, it is more difficult 
to realize it. The body, as a whole, stands still, and we can 
not see the motion of the molecules. But this molecular 
motion is quite as important as the mass motion, since it is 
the source of all heat and light, and of much that is most 
interesting and beautiful in Nature. It is a motion which 
can not be observed directly, but nevertheless our knowl- 
edge of it is almost as definite and accurate as our knowl- 
edge of the larger visible movements. 



4 PHYSICS 

8. Force. — The human mind has grown into the habit 
of hunting for causes back of all events. Motion is a very 
striking event. The mind, therefore, following its old 
habit, has long hunted for a cause of motion. It has 
found none. . It has, however, imagined a cause, and called 
it Force. 

Force may be denned as that which produces motion or 
pressure. 

We shall have occasion from time to time to use the 
term Force, but we shall always have in mind the observ- 
able reality, motion. 

9. Energy. — A body in motion, or a body in such a posi- 
tion that it is capable of motion, is said to possess Energy. 
The motion may be either mass motion or molecular mo- 
tion : the term Energy applies to both. 

A body can lose energy only by giving its motion to some 
other body, whose total motion will thus be increased. A 
body never loses all of its energy because it never loses all 
of its motion. 

The term " energy " is not open to the same objection 
that " force " is. It is permissible to speak of the visible 
universe as a manifestation of energy. 

10. Matter and Motion. — It is convenient for the pur- 
pose of study to speak of matter and motion as being the 
two elements in every event. But in ^Nature the two are 
not thus separated. Matter is always endowed with motion, 
and we only know motion as manifested in matter. When 
we grow wiser, we shall study the two as one experience. 
They are summed up in the term Energy. 

11. Physics. — The study of events in terms of the mat- 
ter and motion involved in them constitutes physical sci- 
ence. If we direct our attention chiefly upon matter, we 
have that aspect of physical science known as Chemistry. 

Chemistry is the study of the composition of matter. 
If our attention be concentrated upon the motion, we 
have that aspect of the science known as Physics. 



THE CONTENT OF PHYSICS 5 

Physics is the study of motion, and deals with matter 
only as the carrier of motion. 

Physics is sometimes defined as the science of the prop- 
erties of matter, since these depend upon its motions. It is 
also defined as the study of the forces manifested in matter. 
Perhaps it is best defined as the Science of Energy, or the 
study of matter in motion. 

12. Metaphysics. — Turning back for a moment to the 
random series of events named in the opening paragraph, 
we see that in addition to the matter and motion involved in 
them, there is in some of them a certain human element, 
or what we may call a thought element. The express train 
represents a certain amount of matter moving in a certain 
direction at a certain rate of speed, but it also represents 
the intelligence which shapes and guides it, and the pur- 
pose which prompts the event. It is the same with the boy 
throwing the ball, and with the child picking the flower. 
This something, outside the matter and motion of the event, 
which we have called the motive, does not fall within the 
province of physics. It belongs to the domain of Meta- 
physics. 

Metaphysics seeks to find a theory of reality. Physics 
does not attempt so difficult a search : it limits itself to the 
study of matter in motion, to the study of things as we see 
them, and is not at all concerned with the underlying real- 
ity. We are not concerned in physics with what things 
really are, but solely with their properties and behavior. 
Physics neither offers nor seeks an explanation of the uni- 
verse. It leaves all such problems to metaphysics. 

13. The Eternal "Why."— We shall not, therefore, find 
in physics any answer to the questions : What is matter ? 
What is motion ? What is heat, light, electricity ? Physics 
defines them, but it does not tell what they are, for it does 
not know. Yet we shall try to show throughout the book, 
and notably in the concluding chapters, that the whole value 
of physics is human. It is worth studying, just because it 



6 MYSICS 

does make our world larger and more orderly and more 
beautiful, and not because physical facts have any value in- 
dependent of their human application. 

Problems. — 1. Select five events and analyze them into their 
matter and motion content. 

2. Name one event containing a thought element and analyze as 
before. Can the thought element be expressed in terms of matter 
and motion ? 

3. If a monkey sit on top of a pole, and always face a man who 
walks around the pole, with his face always turned toward the 
monkey, can the man be said to walk around the monkey ? 

4. Are the hub and the rim of a carriage wheel relatively in 
motion or at rest ? 

5. When the dinner bell rings, is it a case of mass or molecular 
motion ? 

6. Can you name any fact of which you are absolutely sure ? 

Reference. 
Emerson's Essay on Nature. 
First Steps in Philosophy : William M. Salter. 



CHAPTEE II 

THE CONSTITUTION OF MATTER 

Apparatus : Specimens of chemical elements and of simple and compound 
bodies. and H generators or cylinders. Eudiometer tube. Hoffman 
apparatus for decomposing water, and a suitable battery. 

14. The Province of Physics. — We have defined matter 
as that which occupies space, and prevents anything else 
from occupying the same space. It is made manifest to us 
through the senses. 

Xow, physics does not deal with matter as such. That 
is the province of chemistry. But physics does deal with 
matter as the carrier or vehicle of motion, and for this pur- 
pose must inquire very carefully into the constitution of 
matter. 

15. Simple and Compound Bodies. — We know matter as 
solid, liquid, and gas. We can make many substances — 
such as water, for example — pass through all these three 
states. But here our power ends. We can not add or sub- 
tract anything. The water remains a stubborn fact in 
whatever state it exists. 

We do observe, however, a marked difference in the be- 
havior of substances. Some of them can not by any means 
now at our command be separated into different substances 
or constituents. We can get but one thing out of such a 
substance, and that is itself. Matter which is thus incapa- 
ble of analysis into anything else is called a chemical ele- 
ment. There are about seventy elements so far discovered. 
A list of them will be found at the end of the chapter. 

7 



8 PHYSICS 

But there are other forms of matter which may be sepa- 
rated into two or more elementary constituents, and are 
therefore called compounds. Their number is infinite, but 
they all consist of combinations of the seventy elements. 
These compounds form nearly all the substances met with 
in every-day life, such as water, foods, wood, cloth, stone, 
brick, etc. 

16. Atoms and Molecules. — We have no direct proof that 
matter is built up of distinct particles or units. As far 
as we can see, it is perfectly continuous, and occupies 
all of the space that it seems to occupy. But certain 
considerations — such as its contraction and expansion, the 
capacity of certain liquids to dissolve solids and gases, 
the ability of nearly all fluids and of some solids to 
transmit light, and many other phenomena which imply 
a large mobility in matter — have led to the thought 
that matter is made up of definite particles or units, and 
for these the names atoms and molecules have been pro- 
posed. 

The atom is the smallest quantity of an element that 
can exist. It is indivisible and indestructible. Atoms of 
different elements have different weights. These are the 
so-called atomic weights of chemistry. 

The molecule contains one or more atoms, and is the 
smallest quantity of matter that can have a separate exist- 
ence. When the atoms are all alike, the molecule is ele- 
mentary, and the substance which it forms is an element. 
When the atoms are unlike, the molecule is compound, and 
the substance is known as a compound body. 

17. Size of Molecules. — It is not possible to see a mole- 
cule, even with the aid of the most powerful microscope. 
Various estimates of the size of molecules have been made 
by different physicists. The illustration given by Lord 
Kelvin is the most familiar. He suggests that if a drop of 
water were magnified to the size of the earth, its molecules 
would appear as large as tennis balls. 



THE CONSTITUTION OF MATTER 



9 



According to Maxwell, the very smallest particle that 
we can see contains from sixty million to one hundred 
million molecules. 

18. Mechanical Mixtures and Chemical Compounds. — 
When we mix together two elements or compounds in such 
a way that their molecules remain unchanged, we call the 
result a mechani- 
cal mixture. This 
is the condition of 
the atmosphere. 
It consists for the 
most part of the 
two gases, oxygen 
and nitrogen, and 
the molecules of 
each gas remain 
distinct and sepa- 
rate. We speak 
of them as being 
free. When, how- 
ever, the sub- 
stances are so 
united that the 
original molecules 
are broken up and 
new ones take 
their place, we call 
the result a chem- 
ical compound. 
Thus, for exam- 
ple, when two vol- 
umes of the gas hydrogen 'are brought into contact with 
one volume of the gas oxygen in the cold, no matter how 
thoroughly they are shaken up, they remain a simple, me- 
chanical mixture. But if now an electric spark be passed, 
or a flame applied, we have an explosion ; the separate 




lllllljlllllllll^ 



Fig. 1. — Eudiometer tube and induction coil. 



10 



PHYSICS 



molecules of hydrogen and oxygen are broken up, and in 
their place we find molecules of water vapor. We may rep- 
resent this graphically as follows : 

H 2 + H 2 +0 2 = H 2 + H 2 0. 
After the explosion our three molecules are built into 
two. Consequently, the water vapor occupies only two 

thirds the volume of the origi- 
nal gases, and is correspond- 
ingly denser. This may be 
illustrated by introducing two 
volumes of H and one volume 
of into an eudiometer tube 
over mercury, and exploding 
the mixture by means of a spark 
from an induction coil. 

19. Physical and Chemical 
Changes. — In terms of the mo- 
lecular theory we call all 
changes in matter physical, 
which leave the molecules the 
same ; and all changes chemi- 
cal, in which the original mol- 
ecules are broken up and new 
ones take their place. 

Thus the passage of water 
through its three states is a 
purely physical change, while 
the decomposition of water into 
hydrogen and oxygen is a chem- 
ical change. The first is illus- 
trated by the melting of ice 
and evaporation of the result- 
ing water. The second can readily be shown by filling a 
Hoffman apparatus with acidulated water and passing an 
electric current through it for some time. Notice that the 
volume of the H is twice that of the 0. 




mm>^ 



Fig. 2. — Hoffman apparatu 
decomposing water. 



for 



THE CONSTITUTION OF MATTER H 

20. Protyle. — The atom which we have described above 
is the chemical atom, and by definition is indestructible. 
It is more reasonable to believe, however, that as we have 
only one power in the universe manifested in the different 
forms of energy, known as heat, light, sound, electric cur- 
rent, etc., so we have only one form of primary matter, and 
that the so-called elements are in reality compounds of this 
one primal unit. The name protyle has been suggested for 
it. According to this view, the chemical atoms are made up 
of still smaller physical atoms, and are consequently com- 
posed of the same primal stuff. They differ from one an- 
other only in their internal architecture, and hence in their 
capacities for motion. The difference in the behavior of 
the chemical atoms is therefore assumed to depend entirely 
upon the number and arrangement of the protyle atoms 
which go to make them up. 

This view of matter is entirely theoretical. No one has 
ever isolated the molecule and atom, much less the physical 
atom of protyle. Nor have we any authentic record of the 
change of one chemical element into another. The old 
alchemists believed in the transmutation of the metals, and 
spent years in the vain attempt to change base metals into 
gold. Modern science hardly expects to accomplish this 
transformation, even though holding the view that iron and 
gold are made up of the same primal stuff. It does believe, 
however, that in the mightier laboratory of Nature such a 
precipitation of the primal matter into our so-called ele- 
ments may have taken place, is perhaps taking place now 
in distant suns and stars, and that under suitable condi- 
tions these so-called elements may resolve again into the 
primal element. 

21. Doubt. — We have spoken of molecules and atoms in 
some of the preceding paragraphs much as if they really 
existed. But modern science believes nothing of the sort. 
At best, our molecules and atoms are only shadows of con- 
ditions in matter which we do not yet understand. The 



12 



PHYSICS 



terms are convenient, and we must often use them, but 
they must be understood to be names for our ignorance 
rather than for our knowledge. 

Professor Huxley says : " The primitive atomic theory, 
which has served as the scaffolding for the edifice of modern 
physics and chemistry, has been quietly dismissed. I can 
not discover that any contemporary physicist or chemist be- 
lieves in the real indivisibility of atoms, or in an interatomic 
matterless vacuum." 

And Professor Tait says : " An exact or adequate concep- 
tion of matter itself, could we obtain it, would almost cer- 
tainly be something extremely unlike any conception of it 
which our senses and our reason will ever enable us to 
form. . . . The discovery of the ultimate nature of matter 
is probably beyond the range of human intelligence." 

22. The Firm Ground in Physics. — The fact that matter 
and motion must ever remain a profound mystery does not 
make the science of physics any less exact. It deals, not 
with the ultimate nature of matter and motion, but with 
their every-day manifestations, and these are capable of 
exact study and measurement. 

23. Table of Elements. 







State at 








<2> 


Name. 


o 

a 


usual tem- 
perature 

and 
pressure. 


Source. 


Atomic, 
weight. 


Specific 
gravity. 


eg o 

Q 


Aluminium 


Al 


Solid. 


Clay, etc. 


27.0 


2.58 


1828 


Antimony 


Sb 


a 


Sulphid ores. 


120.0 


6.7 


1450 


(Stibium). 














Arsenic 


As 


" 


(t cc 


75.0 


5.71 


1694 


Barium 


Ba 


" 


Heavy-spar, etc. 


137.0 


3.75 


1808 


Bismuth 


Bi 


« 


Sulphid ores. 


208.9 


9.8 


1450 


Boron 


B 
Br 


Liquid. 


Borax. 
Seaweed, etc. 


11.0 
79.95 


2.6 
3.19 


1808 


Bromine 


1826 


Cadmium 


Cd 


Solid. 


Zinc ores. 


112.0 


8.65 


1817 


Ccesium 


Cs 


" 


Alkali salts. 


132.9 


1.88 


1860 


Calcium 


Ca 


" 


Limestones, etc. 


40.0 


1.7 


1808 


Carbon 


C 




Diamond, graph- 
ite, coal, etc. 


12.0 


Up to 
3.5 


Anti- 
quity 



THE CONSTITUTION OF MATTER 



13 



Table of Elements (continued). 







State at 








.23 


Name. 


O 

a 
I 


usual tem- 
perature 

and 
pressure. 


Source. 


Atomic 
weight. 


Specific 
gravity. 


2b 

St 
P 


Cerium 


Ce 


Solid. 


Rare earths. 


140.2 


6.7 


1803 


Chlorine 


CI 


Gas. 


Common salt, etc. 


35.45 


2.45 


1774 


Chromium 


Cr 


Solid. 


Chrome iron ore. 


52.1 


7.3 


1797 


Cobalt 


Co 


" 


Sulphid ores. 


59.0 


8.96 


1733 


Columbium 


Cb 


" 


Rare minerals. 


94.0 


7.+ 


1801 


Copper 


Cu 




NatiYe and sul- 
phids. 


63.6 


8.9 


Anti- 
quity 


Erbium 


Er 


" 


Rare earths. 


166.3 




1843 


Fluorine 


F 


Gas. 


Fluor-spar, etc. 


19.0 




1771 


Gadolinium . . . 


Gd 


Solid. 


Rare earths. 


156.1 




1886 


Gallium ...... 


Ga 


K 


Zinc ores. 


69.0 


5!95 


1875 


Germanium . . . 


Ge 


u 


Rare minerals. 


72.3 


5.47 


1886 


Glueinum 


Gl 


(1 


Beryl, etc. 


9.0 


1.85 


1828 


(Beryllium). 














Gold 


Au 




Native. 


197.3 


19.3 


Anti- 


(Aurum). 


quity 


Hydrogen 


H 


Gas. 


Water, etc. 


1.0 


.069 


1766 


Indium 


In 


Solid. 


Rare minerals. 


113.7 


7.4 


1863 


Iodine 


I 
Ir 


IC 


Sea water, etc. 
Native. 


125.85 
193.1 


4.95 
22.4 


1811 


Iridium 


1803 


Iron 


Fe 


« 


Oxide ores. 


56.0 


8.0 


Anti- 


(Ferrum). 


quity 


Lanthanum . . . 


La 


" 


Rare minerals. 


138.2 


6.1 


1839 


Lead 


Pb 


" 


Sulphids, etc. 


206.95 


11.36 


Anti- 


(Plumbum). 












quity 


Lithium 


Li 




Alkali springs 
and Li mica. 


7.02 


.585 


1817 


Magnesium 


Mg 


<( 


Limestones, etc. 


24.3 


1.75 


1829 


Manganese 


Mn 


" 


Oxide ores. 


55.0 


7.2 


1774 


Mercury 


Hg 


Liquid. 


Native and sul- 


200.0 


13.596 


Anti- 


(Hydrargyrum) . 






phid. 


• 




quity 


Molybdenum.. . 


Mo 


Solid. 


Sulphid. 


96.0 


8.6 


1782 


Nickel 


Ni 


M 


Sulphids, etc. 


58.0 


8.9 


1751 


Nitrogen 


N 


Gas. 


Air and saltpetre 


14.03 


.96 


1772 


Neodymium . . . 


Nd 


Solid. 


Rare earths. 


140.5 


6.5 


1885 


Osmium 


Os 


" 


Native. 


190.8 


22.48 


1803 


Oxygen 





Gas. 


Air, water, and 
most minerals. 


16.0 


1.1056 


1774 


Palladium .... 


Pd 


Solid. 


Native. 


106.6 


12.1 


1804 


Phosphorus . . . 


P 


« 


Phosphate earths 


31.0 


1.84 


1669 


Platinum 


Pt 


k ' 


Native. 


195.0 


21.5 


1741 


Potassium 


K 


c{ 


Chlorid, etc. 


39.11 


.86 


1807 


(Kalium). 














Praseodymium. 


Pr 


M 


Rare earths. 


143.5 


6.5 


1885 


Rhodium 


Rh 


M 


Native. 


103.0 


12.1 


1804 



14 



PHYSICS 





Table of . 


Elements (continued). 










State at 








» 


Name. 


o 
S 

Rb 


usual tem- 
perature 

and 
pressure. 


Source. 


Atomic 
weight. 


Specific 
gravity. 


1° 




Rubidium 


Solid. 


Alkali minerals. 


85.5 


1.52 


1860 


Ruthenium .... 


Ru 


" 


Rare earths. 


101.6 


12.26 


1845 


Samarium 


Sm 


« 


" " 


150.0 




1879 


Scandium 


Sc 


a 


«( a 


44.0 




1879 


Selenium 


Se 


a 


With sulphids." 


79.0 


4.5 


1817 


Silicon 


Si 


" 


Quartz, etc. * 


28.4 


2.48 . 


1823 


Silver 


As 


" 


Native and ores. 


107.9 


10.5 


Anti- 


(Argentum). 












quity 


Sodium 


Na 


" 


Common salt, etc. 


23.05 


.97 


1807 


(Natrium). 














Strontium . ... 


Sr 


" 


Carbonate, etc. 


87.6 


2.5 


1808 


Sulphur 


S 




Native, and as 
metallic sul- 
phids. 


32.06 


2.07 


Anti- 
quity 


Tantalum 


Ta 


" 


Compound ores. 


182.6 


10.+ 


1802 


Tellurium 


Te 


" 


With sulphids. 


125.0 


6.23 


1782 


Terbium 


Tb 


t< 


Rare earths. 


160.0 




1843 


Thallium 


Tl 


" 


" " 


204.18 


11.19 


1862 


Thorium 


Th 


(< 


" " 


232.6 


11.23 


1828 


Thulium 


Tu 


" 


K M 


170.7 




1879 


Tin 


Su 


a 


Tinstone. 


119.0 


7.25 


Anti- 


(Stannum). 


quity 


Titanium.. 


Ti 


a 


Rare minerals. 


48.0 




1789 


Tungsten 


W 


u 


Lead and other 


184.0 


19.26 


1781 


(Wolframium). 






ores. 








Uranium 


u 


u 


Oxide ores. 


239.6 


18.69 


1789 


Vanadium 


V 


a 


Ores of lead, etc. 


51.4 


5.87 


1830 


Ytterbium . . . . 


Yb 


" 


Rare oxides. 


173.0 




1878 


Yttrium 


Yt 


" 


U U 


89.1 




1828 


Zinc 


Zn 
Zr 


« 


Zinc blende, etc. 
Rare oxides. 


65.3 
90.6 


7.12 
4.15 


1520 


Zirconium .... 


1824 



Note.— The common elements are printed in small capitals, the rare elements 
in italics, and the remainder in ordinary type. The table follows F. W. Clarke, 
chemist of the United States Geological Survey. 

Problems. — 1. Select half a dozen common substances, and find 
out whether they are simple or compound. 

2. Is brass a mechanical mixture or a chemical compound ? 

3. Write out the chemical reaction that will express the decom- 
position of water, starting out with two molecules and representing 
them by 2H 2 0. 

4. When a steel bar is magnetized, is the change physical or 
chemical ? 



CHAPTER III 

PROPERTIES OF MATTER 

Apparatus : A set of minerals, representing the scale of hardness. Crystal 
models and, if possible, common crystallized minerals. Balance and 
suspended plate of glass (29). Jars of O and H. Solution of copper sul- 
phate. Diffusion apparatus (34). Dialyzer. Capillary tubes. Mercury. 

24. Secondary Properties of Matter. — In addition to its 
essential properties, extension and impenetrability, matter 
exhibits certain characteristic secondary properties. These 
are so named because they do not, like the essential prop- 
erties, apply to all matter, but only to certain forms of 
matter. Thus, solids possess hardness, crystalline form, 
cohesion, adhesion, porosity, flexibility, elasticity, brittleness, 
malleability, ductility, and tenacity, while fluids exhibit 
diffusibility, viscosity, and capillarity ; and all bodies — solid 
or fluid — separated in space, tend to move toward one an- 
other, a relation which we express by the word weight. 

AVe may not say, however, that weight is an essential 
property of matter, since it is rather a relation than an in- 
dwelling property. A single body, alone in space, would 
have no weight. 

Nor may we properly say that inertia is an essential 
property of matter, meaning by inertia the tendency of a 
body to remain in motion or at rest unless influenced by 
some other body, for this is simply to say that nothing 
happens without a cause — a statement that goes without 
saying. 

Many of these secondary properties of matter are suf- 
ficiently explained if we simply know the meanings of the 

15 



16 PHYSICS 

words themselves. Physics studies only those properties 
which are capable of measurement, or which take some 
knowable part in the drama of natural events. 

25. Hardness. — By the hardness of a body we mean the 
difficulty of penetrating between its particles. We measure 
hardness by comparing bodies with a series of solids ar- 
ranged by agreement in an ascending scale. That most 
commonly in use was proposed by Mohs, and is as follows : 

1. Talc (soapstone). Easily scratched by the finger nail. 

2. Gypsum. Scratched by the nail. 

3. Calcite. Easily cut by knife. 

4. Fluorite. Cut by knife. 

5. Apatite. Difficultly cut by knife. 

6. Feldspar. Cut by glass. 

7. Quartz. Cuts glass. 

8. Beryl. 

9. Corundum. 
10. Diamond. 

This scale was meant for the use of mineralogists, and 
selects natural minerals rather than artificial products, 
partly because they are better suited to the purposes of 
mineralogy, and partly because their hardness is more con- 
stant. 

The test of hardness is very important in determining 
minerals. Thus calcite (crystallized marble, CaC0 3 ) and 
quartz (rock crystal, Si0 2 ) have the same crystal form, and 
often look much alike. A simple test with the penknife 
serves to distinguish them. 

26. Crystalline Form. — Many solid bodies exhibit definite 
geometric forms or crystals. The study of crystals — crys- 
tallography — is a very useful and a very beautiful branch 
of natural science. It is not known why substances take 
definite crystal forms. In doing so they usually increase 
in volume, as when water crystallizes into ice, and the pres- 
sure exerted by their particles is very great ; pipes of lead, 
and even of wrought iron, burst with the freezing of the 



PROPERTIES OF MATTER 



17 



water that they contain ; the hardest rocks are split and 
torn into the tiny fragments which constitute soil, when 
the water in their crevices freezes ; and the delicate lines 
in our printing types are filled out by the expansion of the 
crystallizing type metal. 

Substances which have a cystalline structure often show 
a decided tendency to split along planes parallel to well- 
defined crystal faces. We call this cleavage. It is well 
seen in such minerals as mica, calcite, and feldspar. 

Substances such as flint and opal, which show no crys- 
talline structure, are called amorphous. 

27. Cohesion is the name given to the bond which holds 
the molecules of a body together. It is strongest in solids 
and least in gases. The varying strength of cohesion gives 
us the different degrees of rigidity, tenacity, and hardness 
in bodies. When we break a substance we conceive that 
the molecules become so far separated that their cohesion 
is overcome. Once 
separated, cohesion 
can only be restored 
by bringing the mole- 
cules very close to- 
gether again by some 
agent, such as heat. 
This is done when 
two pieces of wrought 
iron are welded to- 
gether. The same 
thing takes place in 
the working of glass. 

The strength of 
materials depends up- 
on their cohesion. It 
is measured by the number of pounds, or kilogrammes, re- 
quired to break a bar of given cross-section, usually a square 
inch or a square centimetre. When the weight is applied 
3 




Fig 



3. — Showing adhesion between glass and 
water to be greater than cohesion in water. 



18 PHYSICS 

as a pull, we measure the tensile strength of the material. 
When applied as pressure, we measure the compression 
strength. 

28. Adhesion is the general name given to the bond ex- 
isting between unlike molecules — that is, between the mole- 
cules of different substances. When a glass rod is dipped 
into water, a thin film of the liquid spreads itself over the 
glass, and the attraction between the two is considerable. 
We can measure adhesion if we balance a pane of glass so 
that its under surface just touches the surface of the water, 
and then add weights until the glass is pulled away. In the 
same manner light articles, such as pieces of tissue paper, 
feathers, and the like, will stick to the hand and to one 
another. 

29. Elasticity. — When a body has its form altered by 
either a pull or by pressure, the result is called a strain, and 
the pull or pressure itself is spoken of as the stress. If, 
when the stress is removed the strain also disappears, the 
body is said to be elastic. Such is the case with rubber, 
whalebone, and many other substances. If the strain always 
disappears when the stress is removed, no matter how great 
the stress may be, the body is said to be perfectly elastic. 
Fluids are the only bodies which fulfill this condition. No 
solids are perfectly elastic. The degree of their elasticity is 
measured by the coefficient of elasticity. This is the weight 
which would be required to stretch a bar of unit cross-sec- 
tion (such as one square centimetre) to twice its original 
length, were that possible, and still have the bar regain its 
original length when the stress is removed. 

30. Malleability. — -When the molecules of a body are so 
arranged, or so related to one another, that we may pound 
the body into thin sheets without breaking it, we describe 
the body as malleable. Gold is probably the most malleable 
of all substances. It has been beaten into leaves so thin that 
one hundred and twenty thousand were required to make a 
pile one centimetre high. 



PROPERTIES OF MATTER 19 

31. Ductility expresses the arrangement of molecules of 
a body which permits it to be drawn into small rods and 
wire. Platinum possesses this property in a marked de- 
gree. 

The finest wires are obtained by coating a platinum wire 
with silver, then drawing it out as fine as possible, and dis- 
solving off the silver by means of nitric acid. 

Both malleability and ductility depend upon the possi- 
bility of rearranging the molecules of a body within such 
narrow limits that the bond between them — that is, their co- 
hesion — will not be broken. This possibility depends upon 
several factors, such as temperature and purity of material. 
Even small quantities of arsenic or antimony will seriously 
interfere with the working of copper ; and sulphur and phos- 
phorus have a similar effect upon iron.* 

32. Viscosity and Brittleness. — Xo substances, even among 
solids, are perfectly rigid. In all matter the molecules have 
more or less ability to change their relative positions, and 
consequently the body containing them to change its form. 
On the other hand, no substances, even among gases, are 
perfectly fluid. In all there is more or less retardation of 
motion due to an apparent friction among the molecules 
themselves. 

This property of matter is called viscosity. In solids it 
makes permanence of form impossible. A straight glass rod, 
resting for some time upon two supports, gradually assumes 
a curved form under the stress of its own weight. An iron 
girder, between two piers, takes a permanent sag. A cane, 
standing in the corner, becomes crooked. 

In fluids viscosity comes in as a constant retardation to 
motion. Streams do not at once seek their lowest levels, 
but take an appreciable time. Waves do not continue in- 
definitely, but finally spend themselves, overcome by the fric- 
tion of the fluid itself, their motion turned into heat. Fine 

* See Chemistry. 



20 PHYSICS 

particles remain suspended in water and air for a long time, 
their weight being insufficient to overcome viscosity. Storms 
finally spend themselves. 

When a stress acts upon a solid, either as pull or pres- 
sure, in such a way as to make this rearrangement of mole- 
cules impossible, the particles separate, and we call the body 
brittle. 

33. Diffusibility. — We conceive that the molecules of all 
matter are in a constant state of motion. In consequence 
of this activity, two gases or two liquids capable of mixing, 
when placed in communication with each other, 
will become evenly distributed throughout the 
total volume. This diffusion can be shown by 
several simple experiments : 

a. Oxygen is. sixteen times as heavy as hydro- 
gen. When brought together they form 
a highly explosive mixture. If an in- 
^yfe§£ verted jar of hydrogen be placed above 

F"^ a^ a jar of oxygen, the glass cover plates 

7„ . „ withdrawn, and the two iars allowed 

Fig. 4.— Diffusion of _ . ' . ,. „ , 

oxygen and hydrogen, to stand in communication lor several 

hours, it will be found that, in spite of 

their differences in weight, the two gases have thoroughly 

diffused and each jar contains an explosive mixture. On 

separating the jars and applying a match, two almost equally 

loud reports are heard. 

b. If clear water be carefully added to the top of a tum- 
bler already partly filled with colored water, such as a solu- 
tion of copper sulphate, and the whole allowed to stand for 
some time, it will be found that the color distributes itself 
almost equally throughout the tumbler. 

This diffusion of fluids takes place even when the two 
are separated by a porous partition. In general, the lighter 
fluid passes through more quickly than the heavier, as may 
be shown by the following experiment : 

c. An inverted porous cup, such as is used in the Daniell 



PROPERTIES OF MATTER 



21 




cell, has its lower end sealed by a 

tight rubber stopper, through which 

a long glass tube passes. The free end 

of the tube dips under the surface of 

a colored liquid in a tumbler below. 

If, now, a bell jar filled with hydrogen 

be quickly brought over the porous 

cup, the air inside the cup will be 

forced down the glass tube and will 

bubble through the colored liquid. 

The hydrogen makes its way through 

the porous cup faster than the heavier 

air can make its way out. When the 

bell jar is removed, the reverse takes 

place. The hydrogen inside the cup 

escapes faster than the air can take 

its place, a partial vacuum is pro- 
duced, and the colored liquid rises in 

the tube. 

d. In the same way liquids diffuse 

into each other through unglazed earthenware, parchment 

paper, and other porous partitions. The action is known as 

osmose. Dissolved solids have the same power, provided 

they are crystallizable. Amor- 
phous substances, or colloids, 
do not diffuse. Chemists some- 
times make use of this dif- 
ference of behavior to sepa- 
rate some crystallizable poison, 
such as arsenious acid, from 
the amorphous contents of the 
stomach of an animal supposed 
to have been poisoned. The 
process is known as dialysis, 
and is easily carried out in the 
Fig. 6.— Diaiyzer. apparatus (dialyzer) shown. 



Fig 



5. — Diffusion of hy- 
drogen through porous 
cup. 







22 



PHYSICS 










Fig. 7. 



-Capillary elevation and 
depression. 



34. Capillarity. — If tubes of very small diameter are partly 
immersed in water or other liquid which wets them, it will 
be noticed that on withdrawing them in part the leyel of 

the liquid in the tubes is con- 
siderably above that outside, 
and is higher as the diameter 
of the tubes is smaller. In 
case of mercury or other liquid 
which does not wet the glass, 
there is a depression of level 
in the tubes in place of ele- 
vation. 

The same appearances may 
be seen when solids and liquids 
come into contact. The water in a tumbler rises around 
the edge, and the surface of the liquid is concave. Mer- 
cury, on the contrary, would be depressed around the edge 
of the tumbler, and would present a convex surface. Drops 
of mercury on a table take the form of globules. Water 
behaves in the same way if the table be greasy or dusty. 

Since these elevations and depressions are most notice- 
able in hairlike or capillary tubes, the name capillarity has 
been applied to the phenomena. They appear to be strict- 
ly molecular phenomena, and 
to depend upon the relative 
strength of cohesion and adhe- 
sion. Where the cohesion with- 
in the liquid is stronger than 
the adhesion between the solid 
and liquid, the resulting strain 
shows itself as capillary depres- 
sion ; but where the adhesion 
between solid and liquid is the stronger, the strain is a 
capillary ascension. 

We find many illustrations of capillary action in Nature 
— such as the rising of oil in the wick of lamps ; the curi- 





Fig. 8. — Capillary curves. 



PROPERTIES OF MATTER 23 

ous efflorescence of salt over the edge of the tumbler when 
salt water evaporates ; and the wetting of the whole towel 
when one corner is left in a basin of water. 

Experiments. — 1. Try the hardness of such stone and building 
material as may be convenient — marble, brownstone, brick, etc. 

2. Determine the hardness of pyrite, garnet, graphite, and any 
other common minerals that may be within reach. 

3. Let the teacher or pupil, or both, repeat the experiments a, b, 
c, and d (33), and also those under capillarity (34). 



CHAPTER IV 

ON MEASUREMENT 

Apparatus : Yardstick, pound weight, quart measure. Metric units, 
metre, gramme, and litre. Metric chart. A good scale, weighing up to 
several pounds. English and metric weights. 

35. Science is exact knowledge. This is only gained 
by comparison or measurement. " We have only so much 
science as we have mathematics." The first step, therefore, 
in the study of practical physics is to learn how to measure. 

Measurement involves two processes : 

1. The establishment of a standard or unit of measure- 
ment with which we can compare our unknown quantity. 

2. The method by which we carry out this comparison. 
36.* Units. — The choice of standard units must naturally 

depend upon what we wish to measure, and our units must 
necessarily be as numerous as the qualities measured : one 
unit for length, as the yard; another for volume, as the 
gallon ; another for weight, as the pound ; and so on. 

The objection to these common English units, however, 
is that they bear no easily expressed relation to one another, 
and consequently it is quite inconvenient to translate one 
unit into another — as cubic yards into gallons. 

The best system of measurement is that in which the 
different units are simply related, and are easily deducible 
the one from the other. The metric system is such a scheme 
of measurement, and is therefore always used in scientific 
work. In it the unit of mass depends upon the unit of vol- 
ume, and this in turn upon the unit of length. When we 
establish the unit of length, therefore, we establish the others. 
24 



ON MEASUREMENT 25 





Metric Tables. 




Length. 


1 millimetre = 


.0393 inches. 


1 centimetre = 


.3937 " = 10 millimetres. 


1 decimetre = 


3.9370 " = 10 centimetres. 


1 metre = 


39.37 " = 10 decimetres. 


1 kilometre = 


.62137 miles = 1,000 metres. 


1 inch 


= 2.54 centimetres. 


lfoot 


= 30.48 


1 yard 


= 91.44 


1 mile 


= 1,609.33 metres. 



Volume. 
1 cubic decimetre = 1,000 cubic centimetres = 1 litre = 1.0567 quarts. 
1 quart = .9462 litres = 946.25 cubic centimetres. 

Mass. 
1 gram = 15.4323 grains. 
1 kilogram = 1,000 grams = 2.2046 pounds (avoirdupois). 

1 ounce (avoirdupois) = 28.349 grams. 

1 pound " =453.5926 " 

1 ton " =907.185 kilograms. 

In physics we measure both matter and motion. Our 
series of standards, therefore, must be comprehensive 
enough to apply to all measurable aspects of matter and 
motion. By taking a series of related units it is not diffi- 
cult to establish even so far-reaching a system as this, for 
we find practically that only three fundamental units are 
necessary. These are the unit of length, the unit of mass, 
and the unit of time. They form the basis of all physical 
measurement. 

37. Length. — It is unnecessary to define length. We all 
understand by it the distance between two points, or their 
separation in space. The unit of length is the centimetre, 
the one hundredth part of the metre. It was originally 
intended that the metre should be the one forty millionth 



26 



PHYSICS 



part of the earth's meridian. Practically, it is the length 
of a standard platinum bar, copies of which are kept in 
the national archives at Washington, London, Paris, and 
Berlin. 

Most of us are accustomed to thinking of length in 
inches. It may therefore help us to gain a clear idea of the 
centimetre if we remember that it is about four tenths of 
an inch. As soon as possible, however, it will be well to 
think of the centimetre as a unit in itself, and not to trans- 
late it into inches. 

10 Centimeters 



ll lll l ll 



Hlllllil 



Ml" 



llllllll 



I 6 

Inn 



l lll l l l l 



Hill 



T 



1 1 1 m 1 1 I i 1 



■ hi .liiil 



1.1,1,1,1 



h li i i 1 



4 Inches 
Fig. 9. — Comparison of centimetres and inches. 



38. Mass. — The mass of a body is the amount of matter 
it contains. The unit of mass is the gramme. This was in- 
tended to be the mass of one cubic centimetre of pure dis- 
tilled water at the temperature of greatest density. Prac- 
tically, it is the one thousandth part of the standard 
platinum kilogramme, copies of which are also kept in the 
national archives of the several civilized nations. The 
kilogramme is about equivalent to two and one fifth pounds 
avoirdupois. The gramme equals .0352 ounces, and one 
ounce equals 28.35 grammes. 

39. Time. — This can not well be defined, but we all know 
something of the meaning of the word. It is our name for 
the sequence of events. The unit of time is the second. It 
is the -g^Joo P ar t °f an average day (mean solar day). 

40. The C.-G.-S. System. — The system of measurement 
founded on these three fundamental units is known as the 
centimetre-gramme-second system, or, more briefly, as the 
C.-G.-S. system. The units depending on these fundamen- 
tals are called derived units, and are capable of expressing 
all measurable aspects of matter and motion. 



ON MEASUREMENT 27 

41. The Two Terms in Measurement. — It is to be observed 
that every expression of physical magnitude requires two 
terms : One, the numerical term, or coefficient, and the other 
the verbal term, or name of the standard unit, as, for ex- 
ample, 10 centimetres, 8 grammes, 60 seconds. The verbal 
terms are either the fundamental or derived units we have 
been considering, and are agreed upon before beginning the 
measurement. This done, the real process of measurement 
consists in finding the coefficient, or the number of times 
the standard unit is contained in the unknown quantity to 
be measured. 

42. Methods of Measurement. — The comparison between 
the standard unit and the quantity to be measured may be 
made directly or indirectly. 

It is made directly when we apply our foot rule at once 
to the piece of timber to be measured, or when we pour 
water or other liquid into a gallon measure. 

In general, however, our measurements are made indi- 
rectly, as when we find the area of a farm by measuring the 
length of its boundaries, or the temperature of a room by 
observing the length of a column of mercury in a ther- 
mometer. 

Indeed, it seldom happens that quantities can be meas- 
ured directly. In most cases we are forced to resort to in- 
direct methods. It is in devising these that physicists show 
their skill and ingenuity. 

The measurements most open to the direct method are 
those of length, but even here greater accuracy is often ob- 
tained by indirect methods, as when we find the diameter 
of a glass tube from the weight of the mercury which is re- 
quired to fill a given length of the tube, or when we calcu- 
late the diameter of a wire from its length and weight. 

43. Mathematical Physics. — We must then consider mod- 
ern physics simply as an interesting branch of applied 
mathematics. It is a science of measurement, and can be 
studied to best advantage in the laboratory. Practical 



28 PHYSICS 

laboratory work means simply measurement. In the follow- 
ing pages much of our time must be given to the double 
work of establishing a suitable system of derived units, and 
of applying these to the measurement of physical magni- 
tudes. The student who goes to work in earnest should 
first see that he thoroughly understands the unit, and 
should then, as far as possible, make all the measurements 
for himself by which the coefficient that is to stand before 
the unit is determined. Where the facilities of the school 
do not permit the student to make these measurements 
for himself, he should at least see them made, and thor- 
oughly participate in working out the subsequent deter- 
minations. 

44. Conservation of Matter. — It is possible to measure 
matter and to reason about it only because of its persist- 
ence. The sum total of matter always remains the same. 
We can not create it ; we can not destroy it. Our experi- 
ence leads to the belief that its mass is absolutely constant. 
Nor can we even think of matter as coming out of nothing- 
ness, or passing into nothingness again. This all-important 
truth is known as the conservation of matter, and was only 
generally accepted at the close of the eighteenth century. 
We can not prove it by direct experiment, for every method 
would have to start out by assuming what we wanted to 
prove, but reason and general experience are ample proof. 

45. Conservation of Energy. — In like manner it is only 
possible to measure and study motion because of its persist- 
ence. This is a less obvious truth than the conservation of 
matter, for we see on all sides the apparent destruction and 
creation of motion. But a more careful examination shows 
that the disappearance of motion is always followed by its 
reappearance in some other form or in some other body, 
while its seeming creation is in reality a similar transforma- 
tion or transference. We therefore believe that the total 
amount of motion is constant — a truth which we define as 
the conservation of energy. It is only within the past half 



ON MEASUREMENT 29 

century that this truth has been clearly established. It 
has made possible the science of modern physics. 

46. Rationality. — We can not overestimate the impor- 
tance of the recognition of these sister truths, the conser- 
vation of matter and the conservation of energy. If we 
lived in a world in which the amount of matter and motion 
was constantly changing, we should be unable to reason 
about them, or indeed about anything. We should be 
practically insane, for we should be unable to establish any 
relation between the events of life. All would be wild 
chance and caprice. This is much the position to-day of 
those persons who do not realize these fundamental truths. 
They live in a world of unreason and chaos. Judged in this 
way, but a small percentage of the inhabitants of the earth 
are rational. Civilization is only possible because human 
experience is uniform. 

Experiments. — 1. Measure the four dimensions of a sheet of 
paper in millimetres, and express its area in square centimetres. 

2. Measure the length of a rod ten times, take the average re- 
sult, and express the greatest mean error. 

3. Measure a regular-shaped block of wood in millimetres, and 
express its cubical contents in metres. 

4. Measure the linear dimensions of the room you are in, and ex- 
press its volume in litres. 

5. Put a kilogramme weight on the scale, and find its equivalent 
in English measure. 

6. Put a pound weight on the scale, and find its equivalent in 
grammes. 

7. Weigh a quart of water in grammes, and calculate the length 
of tube, one centimetre in diameter, that this amount of water 
would fill. 

Reference. 

Essay on Measurement : William K. Clifford. 
Chapter on Measurement. Practical Physics : Glazebrook & 
Shaw. 



OHAPTEE V 

MEASUREMENT OF MATTER 

Apparatus : Spring compass. Calipers. Micrometer screw. Cathetom- 
eter. Measuring engine. Vernier. Surveyor's tape or chain. Transit. 
Graduated glass jar. 

47. The Problem. — The exact measurement of matter is 
necessary in physics in order that matter may be accurately 
studied as a carrier of motion. The amount of motion we 
have in matter depends upon the amount of matter we 
have moving, as well as upon the rate at which it moves. 
For this purpose the measurements of matter with which 
physics has most to deal are those of extension — length, 
area, and volume — of mass and weight, of density and 
specific gravity. 

48. Extension in One Direction. — The measurement of 
length is of the utmost importance in physical work, not 
only for itself, but also because so many other measure- 
ments depend directly upon it. The process involves no 
theory. It depends entirely upon the precision of the in- 
struments of measurement, and the care with which they 
are employed. The simplest of these instruments is the 
divided scale. For scientific work, its unit is the centi- 
metre and its subdivisions. In determining length, we 
must first make up our minds as to the degree of accuracy 
needed. In comparatively rough work, we apply the scale 
directly, and read off the result with the naked eye, as 
when we measure the length of a line on a drawing, or the 
length of a piece of wood or iron, 

30 



MEASUREMENT OF MATTER 



31 



But this direct method involves two sources of error. 
We can not be sure that the initial division on the scale 
exactly coincides with the beginning of the line to be meas- 
ured, nor can we accurately judge of the fractional subdivi- 
sions of the scale. To avoid one or o'ther or both of these 
sources of error is the purpose of our instruments of preci- 
sion. It is well to make one's self acquainted with several 
of the more important of these instruments. b 

The spring compass, used in every drawing-room, is 
simply a means of transferring a measurement, with great 
accuracy, from line to scale, or scale to line. Yet even so 
simple an instrument is only used accurately after some 
practice. 

The calipers and screw gauge are much alike. Their 
arms, or screw ends encompass the object to be measured, 
and when placed in close con- 
tact with it their distance 





Fig. 10.— Calipers. 



Fig. 11. — Micrometer screw. 



apart is reajl off from the little scale attached to the mov- 
able arm. 

The micrometer screiv is used for determining the thick- 
ness of thin sheets of metal, paper, glass, and the like. It 
consists of a rigid frame of metal, supported by three fixed 
legs. A fourth leg, in the shape of a finely threaded screw, 
turns in a screw bearing in the center of the frame, and is 
provided with a large circular head, accurately divided, so 



32 



PHYSICS 



that one may easily read the fraction of a turn made by the 

screw. If the head makes one complete turn, the leg moves 

through a distance equal to the 

screw thread, and for any smaller 

turn the motion is proportional. 

The micrometer screw may also 
be used as a spherometer, an instru- 
ment for finding the curvature of 
spherical surfaces. 

The cathetometer measures accu- 
rately small vertical distances. It 
consists of a rigid upright scale, 
provided with a sliding telescope 
carrying a second smaller scale. A 
reading is taken when the cross- 
hairs of the telescope exactly coin- 
cide with one end of the distance to 
be measured, and a second reading 
when they coincide with the other 
end. The difference between these 
readings equals the distance. 

The vernier is a device for help- 
ing the eye to read tiny subdivisions 
of a given scale. It is used on 
many instruments of precision. The 
principle is very simple. A definite 
length, say an inch or a centimetre, 
is divided into ten equal parts. A second length is taken, 
equal to eleven of these equal parts, and is itself divided 
into ten parts. If the two scales be laid alongside of each 
other, it is very evident that the subdivisions on the longer 

1 3 3 4 




Fig. 12.— Cathetometer. 



IE 



u_ 



i n i i I 



i i i i i i i i i i i i i i i : 



■ i i ii i i i i 



12 3 4 5 6 



Fig. 13.— Vernier, set at zero. 



MEASUREMENT OF MATTER 33 

scale will overlap those on the shorter scale by just one 
tenth, as shown in the diagram (Fig. 13). Suppose, now, 
that the initial marks on the two scales do not coincide, but 
that the shorter one is four tenths of a division ahead of 
the longer one, as shown in Fig. 14. We shall know the 



12 3 4 

123456789 


, M 1 1 1 1 1 M I 1 1 II 1 1 1 1 MINIMI 1| | || || || 


1 1 1 1 1 1 1 1 1 

^ 1234 5 6789 ^ 



Fig. 14. — Vernier, reading four tenths. 

exact amount by observing that the subdivisions marked 
4 on both scales now coincide, and this can only occur when 
the shorter scale is four tenths ahead. 

49. Surveying. — The instruments already considered 
serve only to measure very short lengths, such as those met 
in the laboratory. In measuring greater lengths, as in sur- 
veying field, or farm, or State, enlarged methods have to 
be adopted. In ordinary farm or railroad work it is suffi- 
ciently accurate to measure distance by means of steel or 
linen tapes, or iron chains. These are generally one hun- 
dred feet long. They are divided into feet, and these again 
into tenths. 

In the case of very, large and accurate surveys, such as 
those made by the United States Coast Survey, generally 
only one length is measured, and the other distances are 
calculated from this. This one line is known as the base 
line, and is measured as accurately as possible. It is some- 
times several miles long. The ground is cleared and lev- 
eled as carefully as if a road were being constructed. The 
length is found by means of rigid measuring rods placed 
end to end, and the contact observed by means of telescopes. 

50. Extension in Two Directions. — We seldom or never 
measure area directly ; that is, by applying the unit of area, 
the square centimetre, to the surface to be measured. In 
nearly all cases we measure the linear dimensions and cal- 



34 



PHYSICS 



culate the area from these by means of the simpler propo- 
sitions in plane geometry. Thus, for example, to get the 
area of a rectangle, we measure the base and altitude. 
Their product equals the area. To find the area of a tri- 
angle we make the same measurements, knowing that half 
the product will be the area. And similarly with other 
surfaces. 

51. Extension in Three Directions. — If the volume to 

be measured is regular in outline, we measure the linear 

dimensions and calculate the volume from 

these by means of the propositions of solid 

geometry. But if the solid be irregular in 

shape, as is generally the case, we can best 

find its volume by immersing it in water or 

other fluid and determirT- 

{ 1 1 ing the volume of the fluid 

3 "■ displaced. 

Examiple. — The volume 
of an irregularly shaped 
stone can readily be found 
by suspending it in a grad- 
uated jar of water. The 
rise of water in the jar will 
indicate the cubical con- 
tents of the stone. Or, 
the jar may be completely 
filled with water, the stone 
carefully lowered into it, 
and the overflow of water 
caught in a measuring 
glass, as shown in figure. 
The volume of fluids is obtained by measuring the 
dimensions of the containing vessel, and then calculating 
its contents. In case the vessel is irregular in form, we can 
find its volume by filling it with some liquid, such as mer- 
cury, weighing the mercury, and then calculating the 




wmmm 



n'w"' 



Fig. 15. — Measuring the volume of a 
stone. 



MEASUREMENT OF MATTER 35 

volume by means of the known relation between the weight 
and volume of the mercury (see Chapter VII). 

As every cubic centimetre of mercury weighs 13.56 
grammes, we have only to divide the weight of the mercury 
in grammes by 13.56 to get the volume of the vessel in 
cubic centimetres. 

Experiments. — 1. Make two dots some distance apart on a sheet 
of paper. Measure the distance five times by direct application of 
the divided scale; take the mean, and see if this corresponds to one 
measurement made by the spring compass. 

2. Determine the thickness of a glass cover plate by means of the 
micrometer screw. 

3. Determine the thickness of a visiting card by the same instru- 
ment. 

4. Measure the diameter of a nickel five-cent piece by the cali- 
pers. 

5. Construct a vernier in stiff paper, making the vernier ji of a 
subdivision on a fixed scale. Do the same, making the vernier 
T 9 o of a subdivision. 

6. Determine the area of a lot or small field. 

7. Find the volume of an irregular-shaped stone or mineral by 
immersing it in water, and measuring the water displaced. 

8. Find the volume of a small test tube by weighing the mercury 
required to fill it. 

Note. — Can you from this weight, and the known length of the 
test tube, calculate its diameter ? 

Reference. 

Gillespie's Surveying, or any other standard work. 
The Coast Survey in Harper's Monthly for March, 1879, vol. 
lviii, p. 506. 



CHAPTEE VI 

MASS AND WEIGHT 

Apparatus : Cubes of the same size, but made out of different material, 
such as cork, wood, clay, metal. A scientific balance, with weights 
from .001 to 50. grammes. 

52. Mass. — We have defined mass as the quantity of 
matter in a body. The unit by which it is measured is the 
gramme. 

If we have two spheres of different size but made of the 
same material, the larger one will of course contain the 
greater mass. In case, however, the material is different, 
the smaller sphere may have the greater mass. We say, 
then, that mass is independent of volume, and we can not 
judge of the mass of a body by simply looking at it, or even 
by measuring its dimensions. 

Suppose, for example, we have half a dozen cubes, made 
of cork, wood, marble, iron, silver, and gold, respectively, 
and each one centimetre in dimension. Their volumes, be- 
ing equal, would be represented by the proportion : 

1:1:1:1:1:1, 
while their masses would be found on experiment to be rep- 
resented very closely by the proportion : 
1 : 3 : 11 : 30 : 42 : 76. 
That is to say, a cube of gold has seventy-six times the 
amount of matter contained in a cube of cork of the same 
size. But while we can not perceive these differences in 
mass by the eye, we do perceive them very readily on han- 
dling the cubes. The greater the mass, the more effort it 



MASS AND WEIGHT 37 

takes to move or lift them. This is our common method of 
judging of the mass of bodies — that is, by what we call their 
weight. 

In general, the weight of a body is directly proportional 
to its mass, but we must be very careful in physics not to 
confound the two terms. The mass of a body is a constant 
quantity no matter where the body may be placed ; while 
the weight is a variable quantity depending upon circum- 
stances. Mass and Weight are therefore two entirely dis- 
tinct expressions, and must never be used the one for the 
other. The reason for this will appear still clearer on con- 
sidering what we mean by weight. 

53. Gravitation. — As far as human experience extends, 
it is found that all bodies in the universe tend to move 
toward one another. We call this tendency gravitation. 
Its intensity depends upon two factors — the quantity of 
matter, and the intervening space, or distance. The 
gravitation between two bodies is greater the larger their 
mass and the smaller their distance apart. This was first 
stated by Newton, somewhat as follows : 

" Every particle of matter in the universe tends to move 
toward every other particle in a straight line joining the 
two, and with an intensity depending directly upon the 
product of their masses and inversely upon the square . of 
their distance apart." 

W^e have no explanation of gravitation. We do not 
know why bodies .tend to move toward one another, and we 
never expect to know. The above statement simply ex- 
presses the observed fact. The name gravitation gives us a 
convenient term by which to refer to the action, but it does 
not explain it. 

54. The Formula of Gravitation.— It is often convenient 
to sum up our observations in a mathematical expression or 
formula. This is simply an exact and short-hand way of 
representing observed facts. Nearly all young students 
strongly object to formulas, under the mistaken belief that 



38 PHYSICS 

they are difficult and obscure. On the contrary, they are 
easy and clear. No great progress can be made in so exact 
a science as physics without their use, and it would be 
well for every student at the very outset to make up his 
mind to understand and use them. This particularly ap- 
plies to gravitation, where we sum up the whole matter 
very briefly as follows : 

m m' 



G 



d* 



in which G stands for gravitation, m and m! for the masses 
of two bodies, and d for their distance apart. It should 
perhaps be added that the distance is measured from the 
center of mass, which is commonly spoken of as the center 
of gravity. In case the body is homogeneous — that is, of 
the same constitution throughout — the center of mass cor- 
responds to the center of figure. 

55. Weight. — In harmony with this universal principle 
of gravitation, all bodies at the surface of the earth tend to 
move toward its center of mass with an intensity depending 
upon their mass and inversely upon the square of their 
distance from the center. 

56. Weight as the Measure of Gravitation. — We can now 
understand why weight is a variable quantity, and we can 
understand it still better if we repeat our formula of gravi- 
tation : , 

p mm 



d 2 

In this fraction, m\ the mass of the earth, and m, the 
mass of the body weighed, are constant, while d, the dis- 
tance from the center of the earth, is constant for any 
one place, but differs for different places. Therefore the 
weight, depending as it does upon G, depends inversely upon 
d, and will also differ in different places. 

As we pass from the equator to the poles we come thir- 
teen miles nearer to the center of the earth, and therefore 
the weight of bodies increases. 



MASS AND WEIGHT 39 

As we ascend high mountains we pass one, two, three, 
four, sometimes over five miles farther from the earth, and 
therefore the weight decreases. 

We may even imagine conditions such that weight would 
disappear entirely. There is a point between the earth and 
the moon where the gravitation toward one body is just 
equal and opposite to that toward the other. A particle at 
that point would practically have no weight. 

But meanwhile the mass has undergone no change. 
At the equator, at the pole, on the high mountain, out in 
space, the quantity of matter was the same. 

We may therefore say that mass is independent of Aveight 
as well as of volume. 

57. Measurement of Mass. — We can not measure mass 
directly, since we can not directly compare our standard 
gramme with the unknown mass to be measured. 

We must therefore measure mass indirectly — that is, by 
some general effect of mass common to all forms of matter. 

Weight is the most convenient measure of mass, and the 
one commonly employed, since weight, as we have just 
seen, is directly dependent upon mass, and is constant for 
any given place on the earth's surface. The practical oper- 
ation of finding the mass of a body consists therefore in the 
process of weighing. 

58. Weighing. — The operation of weighing is carried 
out by means of very delicate balances and very carefully 
standardized weights. It is best learned by practice. It is 
always necessary to test such sensitive instruments before 
using them, as they are very liable to get out of adjust- 
ment. The weights also must be examined from time to 
time and compared with standard weights. 

Two methods are in use — direct weighing and counter- 
poise weighing. 

In the first, the object to be weighed is put in one scale 
pan and the weights in the other. Where the balance is 
accurate, it is the more convenient and better method. 



40 



PHYSICS 



In the second method the object to be weighed is put in 
one scale pan, and fine shot or sand added to the other, 
until the pointer is at zero. The object is then removed, 
and weights put on the scale pan in its place until the 
balance is again even. This method neutralizes any inac- 
curacy in the balance itself. 

The balance commonly used in physical work will weigh 
from several hundred grammes down to the tenth of a milli- 
gramme. The weights of one gramme and over are made 




Fig. 16. — Balance for accurate weighing. 

of brass. Those less than a gramme and down to ten milli- 
grammes are made of platinum, while the milligramme 
weights are made of aluminium, in order that they may 
have greater volume and consequently be easier to handle. 
The fractions of a milligramme are measured by a small 
platinum rider which is placed on the arm of the balance. 
The farther it is moved from the point of support the 
larger value it has. 



MASS AND WEIGHT 41 

When the right weight has been found, and the pointer 
stands at zero, the results should be entered in a notebook 
before the weights themselves are disturbed. This saves 
many mistakes. It is well to take the reading by noting 
what weights are absent from the box, and then verify the 
result when the weights are put back in place. 

Experiments. — 1. Weigh any convenient object first directly 
and then by counterpoising, and compare the results. 

2. Weigh the same object with an added fifty-gramme weight 
on each scale pan, and see if the balance is equally sensitive. 

3. Find the least mass that may be accurately weighed on your 
balance, and see if it is the same when the scale pans are each loaded 
with one-hundred-gramme weights. 

Problems. — 1. If an object could be carried to the center of 
the earth, what would be its weight ? 

2. In going toward the center of the earth, weight at first in- 
creases and afterward diminishes. Why ? 

3. Would a man weigh, more or less, on the moon than on the 
earth ? 

Reference. 

Chapters on the Balance and on Weighing, in Practical Physics : 
Glazebrook and Shaw. 

Other Worlds than Ours, by Richard A. Proctor. 



CHAPTER VII 

DENSITY AND SPECIFIC GRAVITY 

Apparatus : Hydrostatic balance and weights. Distilled water. Eight- 
ounce beakers. Plunger. Specific-gravity bottle of fifty cubic centi- 
metres' capacity. Hydrometers. Alcoholometer. Lactometer. 

59. Density. — We speak of bodies as being light or 
heavy, and by this we mean light or heavy in proportion to 
their size. A small cube of gold contains comparatively a 
large amount of matter, and we speak of gold as being very 
heavy. A similar cube of cork contains little matter, and 
we speak of cork as being very light. This relation be- 
tween mass and volume is known in physics as density. 
Since mass is measured by weight, we may define density 
practically as the weight of a unit of volume of the sub- 
stance. The unit of volume being the cubic centimetre, 
and the unit of mass the gramme, we express the density of 
a substance when we state the number of grammes con- 
tained in one cubic centimetre of the substance. 

The following table gives the density of a number of 
common substances : 

Table of Densities. 

Cork 0.240 

Wood 0.434 to 1.330 

Ice 0.917 " 0.918 

Wax 0.960 

Human body 0.987 

Coal * 1 300 to 1 .500 

Sand 1.420 

Clay 1.900 

42 



DENSITY AND SPECIFIC GRAVITY 43 

Table of Densities {continued). 

ftetort carbon 1 . 90 

Graphite 2.17 to 2.33 

Crown glass 2 . 52 

Marble ? .2.65 

Quartz 2 . 65 

Flint glass 3.00 to 6.00 

Diamond 3.49 " 3.53 

Cast iron 7.00 " 7.70 

Wrought iron 7.80 " 7.85 

Bronze (Cu and Sn) 8.70 " 8.90 

German silver (Cu, Zn, and Ni) 8.30 " 8.40 

Brass (Cu and Zn) 8.20 " 8. 70 

Water 0.99987 

Ether 0. 74000 

Alcohol 0.80620 

Turpentine 0. 97000 

Olive oil . 91000 

Sea water 1 . 02600 

Milk 1.03200 

Air 0.001293 

Carbonic-acid gas 0.001939 

Note. — For specific gravity of single metals and other elements, see 
Table of Elements, pp. 12-14. 

It is to be observed that density varies under different 
conditions. We may increase density by packing the mole- 
cules of a body closer together, as when we roll or hammer 
metals or compress gases. We may diminish density by 
allowing the molecules to separate, as when we expand 
bodies by heat. Hence it is that in stating the density of 
gases we must mention the temperature and also the .pres- 
sure to which they are subjected ; and of solids, the tem- 
perature and the mode of preparation. 

60. Specific Gravity is an expression somewhat similar to 
density and yet not quite identical with it. Specific gravity 
bears much the same relation to density that weight does 



44 



PHYSICS 



to mass. It is our practical measure of the relation be- 
tween weight and volume. 

Specific gravity may be defined as the ratio between the 
weight of a given volume of the substance and the weight 
of the same volume of 9$ second substance taken as a 
standard. 

This is the same as saying that it is the ratio between 
the density of the substance and the density of the standard 
substance. 

The specific gravity of solids and liquids is referred to 
water as a standard. Since the density of water is about 
1, the same numbers express both the density and specific 
gravity approximately of solids and liquids. 

The specific gravity of gases is referred to air as a 
standard, but since the density of air is only .001293, the 
numbers expressing the density and specific gravity of 
gases are far from being the same. 

We shall have nothing to say in this work about meth- 
ods of finding the specific gravity of gases. It will be in- 
teresting to note, however, what is the specific gravity of a 
few of the more familiar ones, as follows : 



Air 1.000 

Hydrogen 0.069 

Oxygen 1.106 

Nitrogen 0.971 

Ammonia 0.537 

Chlorine 3.440 



Carbon monoxide 0.967 

Carbon dioxide 1.529 

Hydrogen sulphide .... 1.191 

Hydrochloric acid ..... 1.254 

Sulphur dioxide 2.247 

Marsh gas 0.559 



The determination of the specific gravity of solids and 
liquids is an operation of much importance. It is com- 
monly carried out by one of the following methods : 

1. The hydrostatic balance. 

2. The specific-gravity bottle. 

3. The hydrometer. 

The second method only will be considered here, the 
first and third being deferred until after buoyancy has 
been treated. . 



DENSITY AND SPECIFIC GRAVITY 



45 



61. Specific-Gravity Bottle. — This is a small glass flask of 
known capacity, usually 50 cubic centimetres, or 50 grammes 
of water. The stopper is accurately ground, so as to fit cor- 
rectly into the neck of the flask, and has a fine capillary bore, 
as shown in the figure, through which the excess of liquid 
may escape when the stopper is pressed into its seat. A 
brass counterpoise is provided which will just balance the 
flask and stopper. The whole purpose of the bottle is to 
provide a means by which we can always measure off pre- 
cisely the same volume of a liquid. It must be used in con- 
nection with an accurate 
balance. The method 
applies to both solids and 
liquids. 

a. Solids. — In this 
case the solid must be in 
small pieces, or in pow- 
der, so that it can read- 
ily be put into the bot- 
tle. A given weight is 
taken, generally about 
five grammes. The bot- 
tle is then carefully filled 
with distilled water and 
the stopper put in place, 
the excess of water es- 
caping through the capil- 
lary tube. The whole bot- 
tle is now thoroughly dried with tissue paper and weighed. 
The specific gravity of the solid can easily be calculated. 
Suppose that just five grammes have been taken, and that 
the bottle has a capacity of just 50 grammes of distilled 
water at the ordinary temperature of the room. When the 
solid is in the bottle, however, the capacity is no longer 50 
grammes of water, but is 50 grammes less the weight of the 
water displaced by the solid. Eepresenting this by m, we 




Fig. 17. —Specific-gravity bottle. 



46 PHYSICS 

shall have 50 + 5 — m = weight found = w, 

or m = 50 -f- 5 — w = 55 — w, 

.„ ., weight in air 

and specific gravity - 



weight of equal volume of water 
5 5 



m 55 — w ' 

It is not necessary that the flask should hold just 50 
grammes, or that we should take just 5 grammes of the 
solid. Indeed, in many cases it is much more convenient 
that we should not do so. If, for instance, we are deter- 
mining the specific gravity of fine wire, and have cut it up 
into short lengths, it will be rather difficult to weigh out 
an even 5 grammes. 

Example. — Silver wire. 

Weight of silver taken 4.984 grammes. 

Weight of water in flask 50.168 " 

Weight of silver and water above 

it in flask 54.679 (to) 

Weight of water displaced by silver 

= 50.168 + 4.984 — 54.679 = .473 grammes (m). 

4.984 
Specific gravity of silver = -jno = 10.52. 

b. Liquids. — The specific-gravity bottle is especially 
adapted for the determination of the specific gravity of 
liquids. The whole process consists in filling the bottle 
carefully with the liquid to be determined, drying it as 
before with tissue paper, and weighing it. This weight 
(omitting, of course, the counterpoise) divided by the 
weight when filled with water, gives the specific gravity. 

Example. — Milk. 

Weight of water in flask 50.00 grammes. 

Weight of milk in flask 51.60 

51.6 
Specific gravity of milk = -^- = 1.032. 



CHAPTEE VIII 

MEASUREMENT OF MOTION 

62. Motion, we have 'seen, is a change of position. To 
study and measure motion we must inquire what elements 
in it are variable. Now, motion is only manifested in bodies. 
We will not, therefore, study motion in the abstract, but 
we will study moving bodies. To do this completely we 
shall have to consider : 

1. The space passed over. 

2. The mass of the moving body. 

3. The time. 

4. The nature of the motion, whether uniform or 
variable. 

5. The path of the moving body. 

The space is simply the length of the path covered by 
the moving body. Where the path is straight — that is, 
where the motion is in a straight line — the space passed 
over is simply the length of a straight line joining the 
original position of the body and its final position. Where 
the path is a broken or curved line, the space passed over is 
the length of this line. In all cases we shall measure the 
space in centimetres, and designate it by s. 

The mass of the moving body is usually expressed in 
grammes and represented by m. 

The time is the number of seconds the body is in mo- 
tion, and is represented by t. 

These three quantities, s, m, and t, are all directly 
measurable by tape-line, balance, and clock. They are the 

47 



48 PHYSICS 

three fundamental units of measurement in the C.-G.-S. sys- 
tem (41). There are relations between s and t, and be- 
tween these two and m, that are highly important. They 
are denned as velocity and as momentum. 

63. Velocity. — If a body move over a space of 50 metres, 
the final result is the same whether the motion takes place 
in a minute or in an hour. But we have not fully de- 
scribed the motion unless we have told the time it occu- 
pies. This rate of motion, or speed, is called velocity and 
is represented by v. We may define velocity as the space 
passed over by a moving body in one second of time. If 
the body be moving uniformly, or if we understand v to 
represent average velocity, we shall have 

s 

V = T 

64. Momentum. — It evidently makes a great difference 
whether the moving body is heavy or light, as we should 
find out very quickly if it struck us. A heavy body has 
more motion in it than a light body, even though both move 
at the same velocity. We define the amount of motion as 
momentum, and represent it by M. It is the product of 
the mass by the velocity : 

M = mv. 

A large body moving with little velocity may still have 
a much greater momentum than a small body moving with 
high velocity, but the effect of the two upon us will be very 
different. The large, slowly moving body will do us no harm 
if we, too, are free to move, because by a very slight effort 
we can give ourselves the same velocity as the body. But 
in the case of the small, rapidly moving body, say a bullet, 
the injury may readily be fatal. Before the bullet can be 
robbed of its momentum, it may penetrate to some vital 
spot. The velocity is so great that we can not hope to 
acquire it ourselves, and so repulse the ballet by going 
along with it. 



MEASUREMENT OF MOTION 49 

65. Nature of the Motion. — Further, motion varies with 
respect to time — that is, is uniform or variable. Motion is 
uniform when the moving body passes over the same space 
each second. Motion is variable when the spaces passed 
over in successive seconds are different. 

Acceleration. — This change of motion may itself be uni- 
form or variable. It is uniform when the increase or de- 
crease in the space passed over in successive seconds — that 
is, the increase or decrease of velocity — is the same. In this 
case, the uniform velocity added or taken away is called the 
acceleration. It is usually represented by a. If a body 
start from a state of rest, and add a velocity of a centi- 
metres each second, it is manifest that its velocity at the 
end of t seconds will be equal to t X «, or 

V=at. 

We may also define acceleration as the rate of change of 
velocity — that is, velocity changes by a centimetres each 
second. 

66. Path of a Moving Body. — A moving body may trace 
any path whatever. The simplest path is, of course, 
a straight line. A boat moving without vibration over 
the surface of still water may trace an almost perfectly 
straight line. But the actual path of bodies is usually 
very much more complex than this. The path of the 
moon is an example. The moon moves around the earth 
in a constantly shifting path. She also moves with the 
earth around the sun. Further, she is probably, along 
with the sun and the rest of the solar system, mak- 
ing a grand tour through space around some other cen- 
ter. The actual path of the moon must be considered 
as compounded of these three and many other separate 
motions. 

We shall consider only the paths described by bodies 
moving in simple straight or curved lines in one plane, and 
the paths described by rotating bodies. 
5 



50 



PHYSICS 



Curvilinear Path. — A body moving in a straight line 
would go on moving in a straight line forever, unless some 
second motion were compounded with the first, and so 
changed the path. We conceive that every curvilinear path 
is the result of compounding two or more motions. The 
most familiar example is that of a projectile of any kind 
thrown into space. Suppose it to be a ball and to be thrown 



PROJECTILE FORCE 




SUN 
Fig. 18.— Motion of earth (E) around the sun. 



horizontally. As we all know, it will approach nearer and 
nearer to the earth, and will finally strike. We explain this 
curvilinear path by saying that the ball has two motions : 
one in a horizontal direction, given by the throw ; and an- 
other in a vertical direction, due to the weight of the ball 
— that is, to gravitation. We may represent this graph- 
ically by the diagram shown in Fig. 19, and this is a very 
convenient way of studying such curvilinear paths. In the 



MEASUREMENT OF MOTION 51 

case of all projectiles the path is a parabola, the curve pro- 
duced when we pass a plane through a cone parallel to one 
of the elements of the cone ; that is, to one of the lines 

joining the apex of the cone ,._- --... 

with some point on the base, -^\« N 

and lying in the surface of the / Nk \ 

cone. / \j\ \ 

In the same way the earth 
may be conceived as having 
two separate motions : one, its 
original projectile motion, if 

we may use such an expression ; \. / 

and the other its motion of con- "" -" 

Stantly falling toward the SUn. Fig. 19.— Motion of ball on end 

By the compounding of these 

two motions, we get a curve, which repeats itself each year, 
and is known as the path or orbit of the earth. This is an 
ellipse, the curve produced when a cone is cut by an oblique 
plane meeting all the elements. 

Similarly a ball or other heavy object attached to the end 
of a string may be twirled around so as to describe a circu- 
lar path. Here the motion of the ball is constantly com- 
pounded with the pull exerted by the string. The ball, 
being kept at constant distance (the length of the string) 
from a fixed point (your hand), is forced to describe a circle, 
since a circle is the locus of all points in a plane at a fixed 
distance from a given point. 

These three paths — circle, ellipse, and parabola — are all 
comparatively simple, but they represent only a few out of 
many possible paths. The study of more complex paths re- 
quires a somewhat full mathematical knowledge, and will 
be found in larger works on mechanics. 

Rotating Bodies. — We have so far assumed that the 
bodies we have been studying were moving freely in space. 
A special case of great practical importance is presented 
when one point of the body is fixed, and the only possible 



52 PHYSICS 

motion is one of rotation, as, for example, a carriage wheel 
or the fly-wheel of a steam engine. Here a series of points 
is fixed, what we call the axis of the wheel, and rotation 
takes place about this straight line. We can not speak of 
the velocity of such a rotating body, since all particles at 
different distances from the axis move with different veloci- 
ties. The usual method of measuring such motion is to 
state the number of rotations per minute. A good average 
dynamo may make 1,200 rotations per minute. 

67. Units of Motion. — We can evidently measure these 
several aspects of motion in the C.-G.-S. system. 

Unit velocity is a velocity of 1 centimetre per second. 

Unit momentum is a mass of 1 gramme moving with unit 
velocity — that is, 1 gramme moving 1 centimetre per second. 

Unit acceleration is unit velocity added or subtracted 
each second — that is, 1 centimetre per second, each second. 

Unit force (F= ma) is a change of unit momentum per 
second, or a change per second of 1 gramme moving 1 centi- 
metre per second. This unit is known as the dyne, and is 
of great importance among physical units. It is commonly 
defined as that force which, acting for one second on 1 
gramme of matter, imparts to it an acceleration of 1 centi- 
metre per second. 

Problems. — 1. What is the velocity in centimetres per second of 
a boy riding a bicycle at the rate of twelve miles an hour ? If the 
road be level and straight, what is his path ? 

2. What is the average velocity of an ocean steamer which re- 
quires six days to run from New York to Liverpool ? Express in 
centimetres per second. 

3. Assuming the boy to weigh 120 pounds, and the steamer 
10,000 tons, compare the momentum of the two bodies. 

4. What is the acceleration of a body which starts from a state 
of rest, and after moving for five seconds has a velocity of 160 feet 
per second ? If, at the end of the five seconds, the same accelera- 
tion, but negative, acted on the body, when would it come to rest ? 

5. A stone attached to the end of a string is twirled around the 
hand. If the string break, what path will the stone describe ? 



MEASUREMENT OF MOTION 53 

6. The fly-wheel of a large pumping engine is making 120 rota- 
tions per minute. If the wheel be twelve feet in diameter, what 
will be the velocity, in centimetres per second, of any point on the 
circumference ? 

7. If the body in problem 4 weighed ten grammes, what force in 
dynes was acting upon it ? 

8. Why does a man running down a beach into the water invaria- 
bly pitch head foremost ? 

9. What path does the rash man describe who jumps from a 
moving street car ? 

Reference. 
Elements of Mechanics, by Oliver J. Lodge. 



CHAPTER IX 

FALLING BODIES 

68. Gravitation (53-56). — All bodies near the surface of 
the earth will, if unsupported, fall toward the surface of 
the earth, or if supported will exert a pressure on the sup- 
port equal to their weight. The term gravitation includes 
both the direct motion of falling bodies and the pressure 
or weight exerted by bodies at re^t. We have already, in 
Chapter VI, considered gravitation as weight ; it remains 
for us to consider it as motion. 

Even Sir Isaac Newton, who investigated gravitation 
with a scientific thoroughness that has left little for subse- 
quent inquirers to find out, declined to assign any cause 
for gravitation, and seems to have believed that it is beyond 
human ken to discover the cause. He was very explicit, 
however, in stating that action at a distance between two 
bodies is unthinkable — that is, he believed that two bodies 
in space can not attract each other across a perfect vacuum, 
and that no one with a philosophical mind would ever think 
such a thing. Our inability to conceive attraction between 
two totally unconnected bodies — that is, our inability to 
explain action at a distance — has made it necessary to fill 
all space with some medium which might serve as a common 
carrier for gravitation and all forms of radiant energy; 
that is, all forms of energy which, like radiant heat and 
light, travel through space in straight lines. This medium, 
the Ether, is supposed to fill all free space and also the 
intermolecular regions of all gases, liquids, and solids. 
54 



FALLING BODIES 55 

There is not a single physical fact which bears direct testi- 
mony to the existence of the ether, but nevertheless it is 
coming to figure more and more prominently in all physical 
discussions, because it enables us to deal with undoubted 
physical facts which we should otherwise be unable to 
handle. The present tendency is to regard gravitation as 
a strain in the ether by which bodies are pushed together, 
rather than as a mutual pull exerted by the bodies them- 
selves. 

The cause of gravitation has naturally aroused the 
curiosity of all thinking minds, but most men, like Newton, 
have put it aside as unknowable. Still, if you go to any 
great scientific library, you will find a few slender volumes 
which venture to discuss the problem. 

69. The Value of g. — Every one knows that the farther a 
body falls the faster it goes. We do not hestitate to jump 
from the top of a fence, but no one is so foolish as to jump 
from a third-story window. Gravitation as motion — that 
is, the actual velocity — is not uniform, but is found by ex- 
periment to increase uniformly in all falling bodies. We 
therefore speak of gravitation as an acceleration (68), and 
since it is a special and very important acceleration, we 
represent it by a special symbol, g. This is the velocity 
added to a falling body each successive second. 

g is not a constant ; at the equator, at sea level, the 
value of g is 978.1 centimetres ; at the poles, at sea level, it 
is 983.1 centimetres. This is partly due to the fact that at 
the poles one is about 21-J- kilometres nearer to the center of 
the earth, and partly due to the fact that at the equator the 
earth's rotation tends to diminish g. If the earth turned 
seventeen times as fast as it does now, g would become 
zero ; if faster than this, objects at the equator would be 
thrown off into space ; g also varies with the altitude, 
being greater at sea level, and less on top of mountains. 

The value of g for all places near the fortieth parallel of 
latitude may be taken as 980 centimetres (about 32 feet). 



56 PHYSICS 

It is the same for all bodies, light or heavy, and only ap- 
pears different on account of the unequal resistance offered 
by the air. In a vacuum all bodies fall with the same 
speed. 

70. Falling Bodies. — The velocity of a falling body de- 
pends directly upon the length of time it has been falling. 
Since the acceleration g is added each second, the velocity 
at the end of t seconds must be t times g. 

v = gt 
Taking g as 32 feet, we should have : 

Velocity at end of 1st second = 32 feet. 

" " " " 2d " = 64 " 

" " " " 3d " = 96 " 

" " " 4th " = 128 " 

" " " " 5th " = 160 " 

The space passed over by a falling body is evidently the 
average velocity, multiplied by the time. The body, start- 
ing from rest, has an initial velocity of zero, and at the end 
of t seconds a final velocity of gt, and the average velocity 
will be the mean of these two : 

+ (ft . ^ 
v = -^- = i gt. 

Substituting this value, we get ' 

s = igtx t = igt*. 

This gives the total space passed over in / seconds. The 
spaces passed over in successive seconds are as follows : 

During the 1st second = 16 feet. 
" 2d " = 48 " 
" 3d " = 80 " 
" 4th " = 112 " 
" 5th " = 144 " 

The formulas give us a ready means of calculating all 
the elements involved in falling bodies. 



FALLING BODIES 57 

71. Projectiles. — We have seen (69) that the motion of 
a projectile is compounded of two motions, the original 
projectile motion and the vertical motion of gravity. If 
we suppose a cannon ball to be fired horizontally from the 
top of a tower, its path would be represented as follows : 

Top of Tower I 2 3 4 



1 second 1 second 1 second 1 second 

Fig. 20.— Path of a cannon ball. 



If the tower were 400 feet high, the cannon ball would reach 
the earth in just 5 seconds. Had it simply been dropped 
from the top of the tower, it would have reached the earth 
in precisely the same time. This seems curious and at first 
sight impossible ; but a moment's reflection will make the 
matter clear. In succeeding seconds the ball drops 16, 48, 
80, 112, and 144 feet respectively, and this whether it is 
moving horizontally or not ; hence in 5 seconds the ball must 
strike the earth. In practice, therefore, the cannon must be 
aimed at a considerable angle above the horizontal in order 
that the ball may carry any great distance. It is in this way 
that modern guns are able to throw a ball 13 miles and over. 
72. Suggestion. — In the preceding paragraph the curva- 
ture of the earth was neglected. The surface was assumed 
to be plane. But, as we know, the surface is spherical, and 
in long-distance surveying this fact must always be taken 
into consideration. If, therefore, we could fire a cannon 
ball with sufficient speed to have the curvature of the earth 
just neutralize the fall due to gravity, and if there were no 
loss of speed by reason of the resistance of the air, and no 
interruption from mountains or other obstacles, our camion 
ball would pass completely around the earth, and would be- 
come a satellite of the earth. 



58 PHYSICS 

What speed would we have to give the cannon ball? 
In 1 second the ball falls 16 feet. To be at the same dis- 
tance above the earth as when it started, the ball must in 
1 second have reached a point where the curved surface of 
the earth is 16 feet below the horizontal line drawn through 
the starting place. This is the case at places five miles 
apart. Hence, our cannon ball to become a satellite of the 
earth would require a velocity of 5 miles a second — that 
is, 26,400 feet per second — and would pass around the earth 
in 1 hour, 23 minutes, and 20 seconds. 

73. Vertical Projectiles. — If a body is thrown straight up 
in the air, its velocity becomes constantly less until finally 
the body comes to rest. Neglecting the resistance of the 
air, it is easy to calculate just how far up the body will 
go. Suppose its initial velocity to be 160 feet per second. 
Then, knowing that gravitation will rob it of 32 feet each 
second, we can readily see that at the end of 5 seconds the 
original impulse will be completely neutralized, and the 
body will momentarily come to rest. It is now 400 feet up 
in the air (s = \ gt 2 ), and starts immediately to fall back 
toward the earth. The return journey also takes 5 seconds, 
and the final velocity will be the same as the initial velocity 
— 160 feet per second. The entire excursion requires 10 
seconds, and the velocity at any point is always the same, 
whether the body be going up or down. 

Problems. — 1 . With what velocity would a man strike the water 
in falling from a bridge 150 feet high ? 

2. How far would a body fall in 10 seconds ? 

3. Through what distance does a body fall during the sixth 
second ? 

4. A stone is thrown upward with a velocity of 100 feet per sec- 
ond ; what velocity has it when 100 feet high ? 



CHAPTEE X 



THE PENDULUM 



74. Importance of Pendulum. — We shall devote a whole 
chapter, though a short one, to the pendulum alone, be- 
cause of its importance in the study of mo- 
tion and of gravity and its application in time- 
keeping. 

We can best study the pendulum by means 
of an ideal instrument known as the simple 
pendulum. While this is purely imaginary, 
the results obtained from such a study may 
easily be applied to the real instrument by 
the addition of a few inconveniences. 

75. The Simple Pendulum. — This consists 
of a heavy metallic bob, M, so homogeneous 
throughout as to have its centre of figure and 
centre of gravity at the same point. We con- 
ceive the entire mass to act as if concentrated 
at this point. The bob is suspended from the 
point of support, 0, by a rigid thread which 
has neither weight nor friction. The length 
of a simple pendulum (I) is the distance, 
M, from the point of support to the centre 
of gravity of the bob. (See Fig. 22.) 

Ordinarily the pendulum will hang in a 
vertical line, M. If M is displaced through 
the angle a to the position M', it will tend to return to its 
original position by virtue of its weight. But when it 
reaches M it has acquired a certain momentum which car- 

59 




Fift. 21.— The 
simple pen- 
dulum. 



60 



PHYSICS 



ries it to the extreme position on the left, M". If it were 
not for the resistance of the air (we have assumed the ab- 
sence of friction) MM" would just equal MM', and the 
pendulum would go on oscillating forever. As it is, the arc 
of displacement becomes gradually less, and the pendulum 
finally comes to rest again at M. 

76. The Motion of the Pendulum. — When displaced, the 
return of the pendulum to the vertical is due not to the 
whole force of gravitation evidently, since the bob is sus-' 



M / 



^ 







Qr"'%\ \\ 






Fig. 22.— Motion of the pendulum. ^"^H 

a u 



pended from and can only move in an arc of a circle 
whose centre is at 0. It must be due to some component 
of gravitation acting along the arc MM'. Let us investi- 
gate the matter. Gravitation can only act vertically down- 
ward, hence we must always represent it by a downward 
vertical line, as M'a. This may be resolved into two com- 
ponents, one (M'd) in the direction of the thread produced, 
and the other (M'b) at right angles to this, and consequently 



THE PENDULUM 61 

tangent to M'M at 31'. The component M'd represents the 
pull on the thread, and is therefore to be neglected. The 
component M'b is that part of gravitation which shows itself 
as motion toward the vertical. As M' descends, the com- 
ponent M'b decreases, and at M disappears entirely. Here 
the entire weight of the bob is exerted as a pull on the 
thread. But the required momentum carries the bob on to 
M", and the component of motion, corresponding to M'b, 
reappears and increases until it overcomes the momentum 
and brings the bob to rest at M". In passing from M" back 
to M' the same course of events repeats itself in inverse order. 

77. Formula of the Pendulum. — The displacement of the 
pendulum on either side of ' the vertical — that is, MM', or 
MM" — is called the amplitude of the vibration. The motion 
is periodic, and is found for small displacements to occupy 
practically the same time. We express this by saying that 
the vibrations are isochronous. It is upon this property 
that the value of the pendulum as a time-keeper depends. 

The time of vibration of a pendulum commonly means 
the time that it takes the pendulum to pass from one ex- 
treme position ( M' ) to the other extreme position (M"), and 
is represented by t. We find its value by developing the 
formula of the pendulum. This can only be rigidly carried 
out by means of higher mathematics, and so we must con- 
tent ourselves here with a simple statement of the formula : 

t — 7T i/~. 

y 9 

78. Discussion of Formula. — This is a very simple for- 
mula, but one which involves large consequences. It shows 
that the time of vibration depends on two things — directly 
on the square root of length, and inversely on the square 
root of g. Consequently, to increase the time two, three, 
four or five fold, we should have to increase the length four, 
nine, sixteen, or twenty-five fold. This can readily be veri- 
fied by experiment. Further, on account of the increase in 



62 PHYSICS 

the value of #, a given pendulum vibrates more rapidly if 
taken from the equator to the poles. 

79. Time-keeping and the Seconds Pendulum. — In the 
Cathedral of Pisa, and right next door to the celebrated 
Leaning Tower, there is still to be seen an antique lamp 
suspended from the roof by a long cord. It is said that 
away back in the year 1582 a boy by the name of Galileo 
noticed that the oscillations of this venerable lamp were 
extremely regular, and he was led to believe were isochro- 
nous. Experiment showed that he was right. By using a 
ball with strings of different length, he also discovered that 
the time varied as the square root of length. It was not, 
however, until 1656 that Huygens made use of the pendu- 
lum to mark time. Each swing of the pendulum is allowed 
to liberate a single tooth of an escapement wheel, and so 
regulates the rate at which the clock hand creeps around 
the dial. 

To find the length of a pendulum which shall beat sec- 
onds at any given place, we have only to make t = 1, sub- 
stitute the value of g for that place, and solve our time 
equation for I. 

l=% (tt = 3.14159.) 

7T 

If g — 980, we have 

I — — s- = 99 cm. (appr.). 

TT 

The length of the seconds pendulum is least at the equator 
and greatest at the poles, but even at the poles it is still a 
little less than a metre. 

80. Determination of g by the Pendulum. — The pendu- 
lum gives us an indirect but at the same time very simple 
and accurate method for determining g. Knowing the 
length of the pendulum, and observing its time of oscilla- 
tion, we have only to solve the time equation for g. 

Itt 2 

9= t *. 



THE PENDULUM 03 

Xearly all determinations of g for practical purposes have 
been made in this way. 

81. The Compound Pendulum. — We can not get a perfect 
bob and still less a rigid thread without weight or friction. 
But the simple pendulum is a capital example of the great 
usefulness of ideal machines in physical investigations. 
The law of the simple pendulum applies equally to the 
real or compound pendulum, if we calculate the length (I) 
of an equivalent simple pendulum. This equivalent length 
for the compound pendulum is the distance from the point 
of suspension to a point called the " centre of oscillation." 
We have seen that the time of oscillation depends on the 
square root of the length. Hence in a real pendulum all 
the particles in the upper part of the rod are retarded, and 
all the particles in the lower part of the bob are accelerated. 
But there must be one point on the axis which is neither 
retarded nor accelerated, and this is the centre of oscilla- 
tion. Huygens found that the centre of suspension and 
the centre of oscillation are interchangeable — that is, the 
time of oscillation is not altered by using either centre for 
the point of suspension. This gives us a practical method 
for finding the centre of oscillation, and so calculating the 
length of the indwelling ideal pendulum. 

Problems. — 1. Will a change of temperature affect the time of 
oscillation of a compound pendulum, and why ? 
2. How could this variation be avoided ? 

Reference. 
For an approximate derivation of the formula of the pendulum, 
see Encyclopaedia Britannica, article Mechanics, paragraphs 51 and 
134 ; and for a rigid derivation see any standard work on higher 
mechanics or advanced physics. 



CHAPTER XI 

COMPOSITION AND RESOLUTION OF MOTIONS 

82. Composition of Motions. — It is evident that a body can 
only move in one direction at one and the same moment ; 
hence if two or more motions are impressed npon a body at 
the same time, these motions mnst be compounded into a 
single motion which represents the actual motion of the 
body. This process of substituting one motion for two or 
more separate motions we call the Composition of Motions, 
and the single motion thus substituted is known as the 
Resultant. It is convenient to represent these motions by 
straight lines which symbolize by their magnitude and 
direction the magnitude and direction of the motions them- 
selves. In addition we must know where the motion starts, 
or its point of application. 

When the motions are in the same direction and have 
the same point of application, the resultant is evidently 
equal to their sum. 

When the motions are opposite in direction and have 
the same point of application, the resultant is their differ- 
ence and is in the direction of the greater motion. 

When, however, the motions are inclined to each other 
in direction and have the same point of application, the re- 
sultant will manifestly take a direction between the two 
motions and inclining to the greater motion. We can find 
its magnitude and direction by representing the two mo- 
tions in magnitude and direction by straight lines drawn 
through a point and then constructing a parallelogram 
64 



B 
Fig. 23. — Parallelogram of motions. 



COMPOSITION AND RESOLUTION OF MOTIONS 65 

upon these lines as adjacent sides. The diagonal will rep- 
resent the resultant. Thus, let the motions A and B have 
a common point of 

application, 0, and O k >\ v 

construct the paral- V ^^\^^ \ 

lelogram A C B. \ ^^^^ \ 

Then C is the re- \ ^^\^^ \ 

sultant. \ ^^*^^ \ 

The figure needs 
no demonstration. If 
we imagine the body 
to have a motion A, represented in magnitude and direc- 
tion by A, it is clear that under the action of that mo- 
tion alone the body would move to A. Similarly, under 
the influence of the motion B alone, represented in magni- 
tude and direction by B, the body would move to B ; but 
as these two motions take place at the same time, the body 
must respond to both impulses and move along a line C, 
which will take it as far down as B and as far to the right 
as A. The point C fulfills both conditions. 

83. Parallelogram of Motions. — This method of finding 
the resultant of two motions is of the utmost importance in 
mechanics. It is called the parallelogram of motions and 
is often stated as follows : 

" If two motions impressed upon a body be represented 
in magnitude and direction by two straight line^ drawn 
through the center of gravity of the body, and a parallelo- 
gram be constructed upon these straight lines as adjacent 
sides, then the resultant motion will be represented in mag- 
nitude and direction by that diagonal of the parallelogram 
passing through the center of gravity." 

It is clear that the parallelogram of motions can be used 
to find the resultant of any number of motions by first find- 
ing the resultant of two of the motions, then compounding 
this resultant with the third motion, then this second result- 
ant with the fourth motion, and so on until all are considered. 
6 



66 PHYSICS 

84. Moments. — If a pull or a push be exerted upon a 
body in a direction passing through the center of the body 
— that is, center of mass or center of gravity — the body if 
free will move along in the direction of the. impulse. But 
suppose, now, that the direction of the pull or push does 
not pass through the center of the body or that one point 
in the body is fixed, what will happen ? 

In the first case the body will evidently turn until the 
direction of motion does pass through the center of gravity, 
and the body will then move in the given direction. 

In the second case the body will turn about the fixed 
point as a center, and will only come to rest when the di- 
rection of motion, the center of gravity, and the fixed point 
are all in the same straight line. 

This tendency to turn about a point has frequently to be 
considered in mechanics, and is measured in a special way 
by means of the mechanical moment. One can not speak of 
the moment of a motion, velocity, or force in the abstract, 
but must always speak of the moment with respect to some 
particular point. The moment is equal to the magnitude 
of the motion, velocity, or force multiplied by the perpen- 
dicular distance from the point to the line of motion, veloci- 
ty, or force. This is illustrated in the following diagram : 




Fig. 24. — Mechanical moments. 

In the first case an irregular stone, whose center of 
gravity is at c, is given motion in the direction a b. The 
moment of the motion a b with respect to c is a b X c d. In 
the second case a crank handle is fixed at c\ and a weight, 
w, is hung from d'. The moment of w with respect to c' is 



COMPOSITION AND RESOLUTION OF MOTIONS 67 



a c b 


A 




> * 
B 


> f 



Fig. 25. 



-Parallel motions in the same 
direction. 



w X c' d'. This perpendicular distance c d or d cT is known 
as the arm of the motion, velocity, or force. 

The device of arms and moments, or, as we say of such 
formal agreements, the convention, is of great use in the 
analysis of machines. 

85. Parallel Motions. 
— When two motions, 
not having the same 
point of application, 
are parallel in direc- 
tion, they will fall into 
one of the three follow- 
ing classes : 

1. The motions are 
in the same direction, 
equal or unequal. 

The resultant is their sum, and the only question is as to 
its point of application. Let A and B be the two parallel mo- 
tions. The resultant R is evidently equal to A -j- B. The point 
of application of R must be nearer to the larger motion B, 
and just in proportion to the relative magnitudes of A and B : 

be : ac = A : B, 
or, A X ac = B X be. 

The moments of A and B with respect to c are equal 
and opposite, and hence both motions are duly represented 
A in R. Had A and B been 

equal, a c and c b would have 
been equal also. 

2. The motions are oppo- 
site in direction and -unequal. 
The resultant is their dif- 
ference, and its point of ap- 
plication must be such that 
the motions A and B have 

26.— Parallel motions in , , .. , 

opposite directions. equal and opposite moments 



1 



Fig. 



68 



PHYSICS 



B 



with respect to the point; consequently it must be some 
point c in a b produced, and such that 

be : ac = A : B, 
or, A X ac = B X be. 

It will seem at first sight as if c should be between a and 
b, but that is impossible, for then the moments of A and 
/ B would re-enforce each other, in- 
stead of neutralizing each other. 

3. The motions are opposite and 
equal. 

This gives rise to a curious sys- 
tem in mechanics, known as a 
couple. In this case A and B, by 
statement, are equal, and if they 
had the same point of application 
their resultant would be zero. But 
separated as they are by the dis- 
tance ab, their effect will be to 
turn a b around until it, too, comes into the vertical and A 
and B are in the same straight line. Hence a couple has no 
resultant. Nor can this rotatory motion be neutralized by 
any single third motion. 
The body can only be 
kept at rest by opposing 
to A B an equal and op- 
posite couple, A' B'. 

86. Resolution of Mo- 
tions. — In the composition 
of motions we substitute 
one motion for two. In 
the resolution of motion 
do the reverse — we 
motions 
processes 



FlG. 27. — Mechanical couple. 




we 

substitute two 

for one. Both 



Fjg. 28. — Besolution of motion. 



are of immense importance in 



physics, And of frequent application. Any motion R may 



COMPOSITION AND RESOLUTION OF MOTIONS 69 

be regarded as the diagonal of a parallelogram OA C B, 
OA' C B\ etc., and may thus be resolved into two motions, 
A and B, A' and B\ or into any other pair whatever, 
which may be represented as the adjacent sides of a par- 
allelogram of which R is the diagonal. 

This may seem like a very indefinite process, since the 
magnitudes and directions of the components may be 
almost anything we like. But in practice the direction 
of one or both components is generally given, and the res- 
olution of R takes a more determinate form. We have 
examples of this in the pendulum, the inclined plane, and 
in many other machines and processes. 

In the same way we may carry out the resolution of ve- 
locities and forces. 

Problems. — 1. Three equal motions imparted to a body leave it 
at rest. What angles do the motions make with one another ? 

2. Four motions are given to a particle : E 24 centimetres, S 36 
centimetres, W 18 centimetres, and N 30 centimetres. Find the 
magnitude and direction of the resultant by means of the polygon 
of motion. 

Reference. 

Elements of Mechanics : Oliver J. Lodge. 

Matter and Motion : J. Clerk Maxwell. 



CHAPTEE XII 

WORK, POWER, AND ENERGY 

87. Work is the overcoming of resistance through space. 
Both elements are necessary to our conception of work. 
Motion through space against no resistance, or a force act- 
ing against a resistance but producing no motion, is doing 
no work. If we represent work by W, force by F, and space 
by s, our fundamental formula for work will be 

W=Fs. 

88. Measure of Work. — In the C.-G.-S. system the unit 
of work will be a unit of force acting through a unit of 
space — that is, one dyne (67) acting through one centimetre. 
Such a unit is called the erg. It is inconveniently small, 
however, and in practice we commonly use a multiple of 
this unit. The joule is 10,000,000 ergs — 10 7 ergs — and for 
most purposes is a more convenient unit. Work is inde- 
pendent of time. An erg or a joule means a definite 
amount of resistance overcome through a definite space, 
but implies nothing with respect to the rate at which the 
work is done. 

89. Power. — It is often important to express not only 
the amount of work done, but also the rate at which it is 
done. This is what we mean by power. It is the rate of 
doing work. The unit of power is unit work done in unit 
time — that is, one erg in one second. It is called the erg- 
second. This, like the erg, is inconveniently small, and is 
also commonly multiplied by 10 7 . The unit so obtained is 
a joule-second, and is called a watt. 

70 



WORK, POWER, AND ENERGY 71 

The Horse Poiver. — The usual units of work and power 
in the industrial world are the foot pound and the horse 
power. The foot pound is the overcoming of one pound re- 
sistance through one foot. As James Watt supposed that 
an average horse could lift 33,000 pounds through one foot 
every minute, he introduced the unit of power known as 
the horse poiver, H. P. It is 33,000 foot pounds per min- 
ute or 550 foot pounds per second. It is equivalent to 746 
watts. 

90. Energy. — It seems, then, that the work of the 
world is done by bodies in motion. Every moving body 
has in it the power of doing work, because by virtue of its 
own motion it can set other matter into motion. This 
power of doing work we call Energy. The whole drama of 
the world, physically speaking, consists in the transfer and 
transformation of energy. Eemembering that energy is rep- 
resented by matter in motion or matter capable of motion, 
we may say that the study of energy is the study of the 
universe. It is for this reason that we have put on the 
title-page of this book, — Physics, the Science of Energy. 
Energy, like work, is measured in ergs and joules. 

91. Forms of Energy.— The ability to do work and the 
effects produced in matter when work is done upon it show 
themselves in various ways and give rise to what are known 
as the forms of energy. These are all intimately related, 
and while it may be convenient at times to study the differ- 
ent forms under such separate headings as mechanical mo- 
tion, sound, heat, light, magnetism, electric current, chemical 
affinity, and the like, we miss the main thought of modern 
physics as we do of modern philosophy if we allow these 
energy forms to take separate shape in our minds and get 
at all far apart. They are but qualities of the one essence 
— energy. We seldom have one of these qualities mani- 
fested alone. Any change in one quality, either in its in- 
tensity or in its continuance, involves similar and compen- 
sating changes in the other qualities. This is the deep 



72 PHYSICS 

truth underlying the doctrine of the conservation of energy. 
You can not create energy or destroy it. Mechanical mo- 
tion may stop, sound may cease, heat may disappear, light 
may he extinguished, magnetism may vanish, electric im- 
pulse may he lost, chemism may spend itself, hut energy — 
the one eternal energy, of which these are the qualities or 
forms — energy goes on forever. 

92. Transfer and Transformation of Energy. — We detect 
on all sides a tendency in energy to react with energy that 
is in a different state of excitement, and to stop reacting 
only when the two states are quite alike. This sums up 
the possibilities in the physical world. Bodies representing 
different degrees of energy meet and react. It is incorrect 
to say that one body acts on another, and to stop there. 
The truth is that both bodies are affected, one as much as 
the other. The reaction only ceases when the bodies possess 
the same degree of energy ; but when this does occur they 
are quite indifferent to each other. Were all energy of the 
same intensity there would be perfect equilibrium. 

93. Newton's Laws. — When the world of science was 
still very young — that is to say, about two centuries ago — 
Newton, with an insight that must always appear marvel- 
ous, expressed the main facts about motion and energy in 
three laws as following : 

First Law : " Every body perseveres in its state of rest or 
of moving uniformly in a straight line except in so far as it 
is made to change that state by external forces " (Cause and 
Effect). 

Second Law : " Change of motion is proportional to im- 
pressed force, and takes place in the direction in which the 
force acts." 

Third Law : " Eeaction is always equal and opposite to 
action — that is to say, the actions of two bodies upon each 
other are always equal and in opposite directions." 

94. Energy — Kinetic and Potential. — Energy is not only 
represented by matter in actual motion and ready to do 



WORK, POWER, AND ENERGY 73 

work on the instant, as a hammer descending, but it is also 
represented by matter in such a position that it is capable 
of motion and ready to do work when the time comes, as a 
hammer poised. The energy represented by matter in 
actual motion is called kinetic ; the energy represented by 
matter capable of motion is called potential. 

Reciprocity. — When a moving body does work by giving 
up a part of its motion, it may be said to have negative work 
done on it. The body acted upon gains the motion lost by 
the body acting, and has positive work done on it. The 
algebraic sum of this negative and positive work is zero. 
In one sense, therefore, no work is ever done in the world. 
Energy is simply transferred. 



CHAPTEE XIII 

MACHINES 

95. A machine is a device. for doing useful work. To 
do work is to overcome some sort of resistance through 
space. It is very obvious that a machine can not do this 
work of itself, but must be energized from without. The 
ability to do work depends upon the motion of the machine, 
and since this motion is so constantly spent in doing useful 
work, the supply must be constantly kept up. The motion 
is supplied by the expenditure of force — chemical, mechan- 
ical, or electrical ; and since the rate of work is also impor- 
tant in all practical operations, the element of time comes 
in, and our force must be expressed in terms of power. 

Hence we may say that a machine is a device for trans- 
forming power into useful work. 

In our analysis of machines we shall speak of the work 
put into them as Power, p, and the useful work got out of 
them simply as Work, w. In this comparison no element 
of time comes in since they proceed simultaneously. If the 
machines were perfect and frictionless, the power put in 
and the work got out would be just equal in amount. But 
some of the power is always lost in doing internal work in 
the machine itself — that is, in overcoming the resistance or 
friction of the several parts. It is not lost in a mechanical 
sense ; it reappears as heat and electricity, or is spent in 
wearing down the bearings. It is only lost in a utilitarian 
sense. The transformation of power into work is always 
effected, therefore, at the cost of some loss of power, and the 
74 



MACHINES 75 

best we can do is to reduce the loss to the smallest possible 
amount. 

The efficiency of a machine is the ratio of work to power 

— that is, and expresses the exact percentage of power 

utilized as work. 

96. Axiom. — You can not get more work out of a ma- 
cltine tlian you put into it. 

Indeed, as we have just seen, you can not get as much, 
but the axiom is worth stating in this emphatic way, for 
it discredits at once all schemes for perpetual-motion ma- 
chines. Perpetual motion itself is not only possible, but 
unavoidable, since motion can never be destroyed. But a 
" perpetual-motion machine " is a contradiction, for it im- 
plies the creation of energy on the part of a mechanism. 

97. The Principle of Virtual Velocities. — But machines, 
though they create no energy, do possess advantages beyond 
their mere ability to transform power into work. While 
the amount of useful work is always less than the amount 
of power consumed, we can accomplish tasks greater in 
magnitude by the use of machines than we could possibly 
accomplish without them. If we are willing to spend power 
over a long period of time and accomplish work at a very 
slow rate, we can move mountains, and justify the boast of 
the old philosopher who said that he could move the world 
if you would only give him a place to stand on. Let us see 
how this is. 

Work = Force X Space, or W = Fs. 

Since work is made up of two factors, force and space, 
we may vary these to suit ourselves, making either one large 
and the other one correspondingly small. Thus, if we make 
s large, F will be small, and our machine will overcome 
only a small resistance, but will do it through a large 
space. On the other hand, if we make s small, F may be 
very large, and our machine will be a veritable Hercules, 



76 PHYSICS 

overcoming tremendous resistance, but doing it through a 
very small space— that is, very slowly. 

Meanwhile the power put into the machine has been a 
constant quantity. This is also represented by force acting 
through space. Machines are said to have a mechanical 
advantage when the force-element in the work is greater 
than the force-element in the power. The difference in the 
spaces passed over preserves the equality between the two 
amounts of energy. We sum this all up in the principle of 
virtual velocities : 

" The force put into a machine, multiplied by the space 
through which it acts, is always equal to the force got out 
of a machine multiplied by the space through which it acts." 

98. Simple Machines. — The five simple machines, known 
as the lever, the wheel and axle, the inclined plane, the 
pulley, and the screw, occur in all sorts of mechanisms, and 
have many important applications in daily life. They may 
be analyzed by means of the principle of virtual velocities, 
or by applying the principle of moments. We shall use 
either method and sometimes both. We shall always rep- 
resent the force put into the machine by p, and the space 
through which it acts by d, and its arm by a. In the same 
way we shall represent the force got out by w, the space 
passed over by s, and the arm by o. (See Fig. 32.) 

The process of mechanical analysis is very simple. It 
consists in finding the relation between^ and iv, and pro- 
ceeds by applying one or both of the fundamental formulae 
of machines : 

1. (Virtual Velocities), pd = ics. 

2. (Moments), pa = tub. 

99. The Lever consists of a rigid bar supported at one 
point, called the fulcrum,/, and capable of turning freely 
about this point. There are three possible arrangements in 
the disposition of fulcrum, pressure, and weight, and this 
gives rise to the three classes of levers : 



MACHINES 



77 




VP 



Fig. 29. — Lever of the first class. 



1. The lever of the first class has/ in the midway, and 
consequently p and iv at the ends. 

2. The lever of the second class has w in the midway, and 
consequently / and p at the ends. 

3. The lever of the third class has p in the midway, and 
consequently / and w 
at the ends. 

Analyzing 1 by 
virtual velocities, we 
have (Figs. 29, 32) : 

7 d 

tvs — pd, or to = -p. 

If d is greater than 
s, there is mechanical 
advantage ; if less than 
s, mechanical disad- 
vantage. In the first 
case the fulcrum will 
be nearer w ; in the 
last case, nearer p. In 
the figure, d is two 
thirds of s, since a is 
two thirds of b ; hence 

— = — , and there is me- 
s 3 

chanical disadvantage. 
Analyzing 2 by mo- 
ments, we have (Figs. 
30, 33) : 

tub = pa, or w = — p. 




Fig. 30. — Lever of the second class. 



HimiiiiiimiiiHiiiiiii 



mum 
/ 



Fig. 31. — Lever of the third class. 



The arm a is the dis- 
tance of p from the fulcrum, and the arm b is the distance of 
w from the fulcrum. It is evident that the moments must be 
taken with respect to /, since that is the only fixed point, 
and consequently any motion must be about / as a center. 



78 



PHYSICS 



In levers of the second class it is evident that there 
must always be mechanical advantage, since iv, having the 
shorter arm, must always be greater than p. 

Analyzing 3 by both 

virtual velocities and 

have 



(i) 




32. — Analysis of the lever of the 
first class. 



W 



di 



! P 



Fig. 33. 



"i 

> 
i 
i 

\p 



-Analysis of the lever of the 
second class. 




Fig. 34. — Analysis of the lever of the 
third class. 



mome 


nts, 


we 


(Figs. 


31, 


34): 




ws 


= pd, 


or 


w 


d 
= ~P 




wl) 


-pa, 
a 



or 



W 



-TV- (2) 



In levers of the 
third class there can 
never be mechanical 
advantage, since p is 
always nearer to /, 
and must therefore be 
greater than w. The 
arms a and b are the ra- 
dii of the circles over 
which p and iv move 
when displaced, and of 
which d and s are the 
actual arcs passed over. 
Since circumferences 
of circles are to each 
other as their radii (c 
= 2 7ir, and c' — 2 7tt'), 
the corresponding arcs 
d and s must be as the 
radii of their respec- 
tive circles — that is, 

— — - ,a relation which 
s o 



MACHINES 



79 



would have to be true if 1 and 2 are both true. The prin- 
ciple of moments is indeed but a special statement of the 
principle of virtual velocities. 

Applications. — These are almost too numerous to men- 
tion. 

First class : Crowbar, balances, walking beam, steel- 
yard, seesaw, scissors (double). 

Second class : Crowbar (when resting against the ground), 
nut crackers (double), wheelbarrow, oars, canoe paddle, 
bicycle pedal. 

Third class : Spring shears, pincers, fire tongs, foot 
treadle. 

Note. — The analysis of the lever is, after all, but a special applica- 
tion of the study of parallel forces. Should the forces of either pres- 
sure or weight be applied obliquely, it would be necessary to resolve 
them into two components, one at right angles to the lever and the 
other in the direction of the lever. We should only consider the com- 
ponent at right angles to the lever, since this would be the only one 
capable of producing motion about 
the fulcrum. It should also be added 
that we have throughout neglected 
the weight of the lever itself. In prac- 
tice this must be taken into consid- 
eration, but the correction may easily 
be made. 



100. The Wheel and Axle.— 

This is practically an application 

of the lever of the second class, 

the fulcrum being the common 

axis of the wheel and the axle. 

Our analysis can best be made 

by help of moments. The arm 

of the weight is the radius of 

the axle, b ; the arm of the pressure is the radius of the 

wheel, a. As before, 




Fig. 35.— Wheel and axle. 



wb 



pa, or w = —p. 



80 



PHYSICS 



The wheel and axle, arranged as shown, will always give 

a ' 
a mechanical advantage expressed by v-. 

The wheel and axle find application in such special ma- 
chines as the windlass and in many complex mechanisms. 

101. The Pulley. — In its simplest form the pulley is a 
fixed wheel, which serves to change the direction of motion, 
but offers no mechanical advantage. As P and W (Fig. 36) 
move through the same distance, they must be equal. 

W= P. 

In this form it is simply a lever of the first class (Fig. 
32), in which a and b are equal. 

Where the pulley is movable (Fig. 37), and one end of 
the rope is fixed at C, the force P moves through twice the 
distance that the weight, W, is raised, and consequently 

W=2P. 





Fig. 36.— Simple 
pulley. 



Fig. 37.— Movable 
pulley. 



Fig. 38.— Series of 
movable pulleys. 



In this form it is simply a lever of the second class 
(Fig. 33), in which a = 2b. 

By arranging a suitable system of movable pulleys, 
almost any mechanical advantage can be secured. It is, 



MACHINES 



81 



of course, at the expense of speed. Each movable pulley 
diminishes the speed one half, and increases the weight that 
any given force can raise twofold. Such an arrangement 
is shown in ' Fig. 38. In this case we 
have the force P multiplied by two for 
every movable pulley employed. Hence 
if n be the number of movable pulleys J 
employed, we shall have 
W=2» P. 
In the figure n = 3, and so W=2 3 P 
= 8 P. 

It is more convenient in practice to 
arrange one fixed block containing sev- 
eral pulleys on the same axle, and one 
movable block also containing several 
pulleys on a common axle. This is 
shown in Fig. 39. Here there is only 
one rope, whose fixed end is attached to 
the fixed block. The rope then passes 
alternately over the pulleys of the two 
blocks, and finally emerges from the 
upper block, passing downward for the 
application of the force P. In this case the fixed pulleys 
in the upper block contribute nothing to the mechanical 
advantage. The pulleys in the movable block add each 
a twofold advantage ; hence, if n be the number of pul- 
leys, the relation will be 

W = 2 n.P. 

102. The Inclined Plane in its simplest form is a device 
for lifting weights which would otherwise be inconveniently 
or impossibly great. It may be analyzed in two ways, 
either by virtual velocities or by resolving the weight into 
two components, one acting along the inclined plane and 
one at right angles to it. In Fig. 40 w is to be lifted 
through the height s, but p may move through d. Hence 




Fig. 39. — Compound 
block pulley. 



82 



PHYSICS 



the advantage is greater the longer d is, with respect to s — ■ 
that is, the smaller the angle of the plane — a. 

i d 

ws = pa, or w = — p. 

s 
As a increases from 0° to 90°, we can easily see that the 
pressure, p, must be increased, as the plane gets steeper, 




F;g. 40. — Inclined plane. 

and will finally equal the weight, w, when the plane is ver- 
tical. Then w — p. 

In Fig. 41 the weight is represented by a straight line, 
c g (which, as we have seen, must always be vertical and 
must start from the center of gravity, c). This is the only 




Fig. 41. — Analysis of inclined plane. 

force acting on the body. But the body can not move in 
the direction of c g. It can only move down the inclined 
plane, and this it will soon proceed to do unless we stop it. 



MACHINES 



83 



Hence the weight eg must be resolved into a component, c I, 
parallel to the plane, and a component, I g, at right angles to 
the plane. This last component shows itself as pressure 
against the plane and does not concern us here. The com- 
ponent, c /, represents the motion down the plane, and must 
be met by a force, I c, equal and opposite to c I, if the body is 
to be supported on the plane. I c represents the pressure, 
or p. Hence, 

w : p : : eg :lc 
w x le — p X eg 

Whichever method of analysis we use, we get the same 
result. 

The Wedge is simply a double inclined plane, in which 
the pressure is exerted at right angles to the common back 
— that is, in the line of the common base. It has applica- 
tion in all our cutting tools, such as the knife, chisel, and 
axe. It has also direct use in splitting timber and in sepa- 
rating layers of rock. 

103. The Screw. — The usual form of the screw, such as 
is seen in a copying press, may be regarded as a combina- 
tion of an inclined plane and the wheel and axle. The 
screw thread is simply an inclined plane wrapped around a 
cylindrical support. The pitch of the screw — that is, the ver- 
tical distance be- 
tween two neigh- 
boring threads — is 
the height of the 
plane. The thread 
corresponding to 
one complete turn 
is the slant length 
of the plane, and 
the circumference 
of the screw corresponds to the base of the plane. The 
force is generally applied to the circumference of a wheel 
mounted on one end of the screw. We can best analyze the 




Fig. 42. — Screw. 



84 PHYSICS 

screw by means of the principle of virtual velocities. Thus 
the force, p, moves through the circumference of a circle, 
whose radius, r, is the radius of the wheel, while the weight, 
w y advances a distance equal to the pitch of the screw. 

ws = pd. 
iv X pitch = p X 2 irr. 

~ pitch ' *' 

By making the wheel large and the pitch small, we can 
get a tremendous mechanical advantage. The screw has 
many applications besides the copying press. By means of 
powerful jack screws, a whole building can be lifted from 
its foundations. The screw is used in the lathe and other 
mechanisms, and in many physical instruments, as the mi- 
crometer screw, to say nothing of its manifold use as clamp, 
fastener, and leveler. 

Experiments. — 1. Take a straight bar of strong, sound wood, 
about 1 metre long and 2.5 centimetres square, and find its weight 
by weighing a simple bar, 5 to 10 centimetres long, and of the 
same cross-section. By this method one can get an accurate result, 
and use a delicate balance. Let this weight be x. 

2. Balance the lever thus obtained on the sharp edge of a trian- 
gular piece of wood, used as a fulcrum, mark the fulcrum/, and see 
if it is in the center of the lever. 

3. Put unequal weights on the ends of the lever ; balance it 
afresh ; measure the two arms, and calculate the moments of the 
two weights. Allowing for the unequal weights of the two arms, 
are the moments equal ? 

4. To weigh the lever by moments. Take the same lever, add a 
suitable weight, w, to one extreme end, and balance, marking this 
fulcrum/'. Designate the distance from w to/' as the arm b. The 
moment is then wb. The force on the other side of /' is the weight 
of the lever, p, and its arm, a, is the distance /'/ since the weight 
of the lever will act as if concentrated at its center of gravity /. 

The moment is pa. wb =pa, or p = — . w. Is this equal to x as 
obtained in Ex. 1 ? 



MACHINES 85 

5. Mark one end of the lever c, and the other end d. Support d 
on the triangular fulcrum, and c by means of a spring balance. Take 
the reading r. Add a known weight, y, to any point of the lever, g, 
and take a second reading, r' . 

Does (r' — r) x cd = y x gd ? 

6. Repeat the experiment, placing the spring balance at g and 
the weight y at c. What now is the result ? 

7. In the same way, take two boards of equal length, I, and sup- 
port as above, with a narrow crack between. Support w by a strong, 
light thread, passed through the crack, and fastened to the spring 
balance. Keeping balance and thread horizontal, determine the re- 
lation between w and p. 

Problem. — 1. Can the wheel and axle be so arranged that it 
will give a mechanical disadvantage ? If not, or if so, explain the 
reason. 

2. Determine the mechanical advantage in the case of the in- 
clined plane, when the force p is applied parallel to the base, giving 
your result in terms of the base and height of the plane. 



BENJAMIN FRANKLIN" (1706-1790) 

Fkanklik was born in Boston, January 17, 1706. At 
seventeen years of age he hired out as a printer in Phila- 
delphia. He became the leading journalist of America. 
For twenty-five years he published Poor Eichard's Almanac, 
which attained a marvelous popularity. 

He acquired familiarity with French, Spanish, Italian, 
and Latin. He became America's leading diplomatist and 
statesman. He was one of the committee of five which 
wrote the Declaration of Independence ; a member of the 
commission appointed to negotiate peace with England at 
the close of the Revolutionary War ; a leading member of 
the first National Convention elected to frame the Con- 
stitution ; and American minister to France for nine years. 

His principal scientific researches were upon balloons 
and atmospheric electricity. He was a member and one of 
the managers of the Royal Society, London, and a mem- 
ber of the Royal Academy of Sciences, Paris. Together 
with a committee of the French Academy, he investigated 
mesmerism at the request of the King of France, which re- 
sulted in the disgrace and flight of Mesmer. 

McMaster, in the History of the People of the United 
States, vol. i, pp. 233 and 422, says : " He was renowned 
throughout Europe as a philosopher ; nor has his just 
fame been cast in the shade by any investigator our coun- 
try has since produced." " Franklin was in truth the 
greatest American then living ; nor would it be safe to say 
that our country has since his day seen his like." 
86 




BENJAMIN FRANKLIN. 



MECHANICS OF FLUIDS 

CHAPTER XIV.— Pressure in Liquids 

104. General Definition of Fluids. 

105. The Mercury Pressure Gauge. Figs. 43 and 44. 

106. Pressure in Terms of Inches of Mercury. 

107. Pressure in Terms of Pounds per Square Inch. Fig. 45. 

108. First Principle. Figs. 46 and 47. 

109. Pressure is due wholly to Gravity. Figs. 48 and 49. 

110. Upward Pressure in Liquids. Figs. 50 and 51. 

111. Liquids seek their own Level. Figs. 52 and 53. 

112. Buoyancy. Figs. 54 and 55. 

113. Specific Gravity. Figs. 56, 57, and 58. 

114. The Specific Gravity of the Human Body. 

115. How Iron Ships Float. 

116. Stability of Floating Bodies. 

CHAPTER XV.— Pressure in Gases 

117. General Behavior of Gases. 

118. Second Principle. 

119. The Atmosphere. 

120. Weight of Air. 

121. The Barometer. Figs. 59, 60, 61, and 62. 

122. The Aneroid Barometer. Fig. 63. 

123. Variations in Atmospheric Pressure. Fig. 64. 

124. Boyle's Law. Figs. 65, 66, and 67. 

125. Closed Pressure Gauges. Fig. 68. 

126. Buoyancy of Air. Fig. 69. 

127. Balloons. 

CHAPTER XVI. — Transmission of Pressure in Fluids 

128. The Transmission of Pressure. 

129. Third Principle. Fig. 70. 

130. Hydrostatic Press. Fig. 71. 

87 



88 PHYSICS 



CHAPTER. XVII. — Applications of Principles of Fluid 
Pressure 

131. The Density of Milk. 

132. The Bottle Imp or Cartesian Diver. Figs. 72 and 73. 

133. Magdeburg Hemispheres. Fig. 74. 

134. The Relation of Tension and Pressure. Fig. 75. 

135. Bacchus Illustration. Fig. 76. 

136. " Siphon " Bottles, Fire Extinguishers, and Explosions. 

137. Diving-bells and Caissons. 

138. The Ear Drum. 

139. The Physics of Respiration. 

140. How Atmospheric Pressure upon the Human Body is Sustained. 

141. The Fountain in Vacuo. Fig. 77. 

142. Pumps. Fig. 78. 

143. Force Pumps. Fig. 79. 

144. Air Pumps. Figs. 80 and 81. 

145. The Mercury Pump. Fig. 82. 

146. The Water Exhaust. Fig. 83. 

147. Air Compressors and Blowing Engines. 

148. Siphons. Figs. 84, 85, and 86. 

149. Siphoning Gases. Fig. 87. 

150. Hero's Fountain. Figs. 88 and 89. 

151. Tension inside the Barometer Tube. 

152. The Inverted Tumbler of Water. Fig. 90. 

153. The Specific Gravity of Liquids measured by balancing them 

against Atmospheric Pressure. Fig. 91. 

154. Fluids in Motion. Figs. 92 and 93. 

155. The Hydraulic Ram. Figs. 94 and 95. 



CHAPTEE XIV 



PRESSURE IN LIQUIDS 

104. General Definition of Fluids. — We designate both 
liquids and gases as fluids, because both are characterized 
by the great mobility of their molecules. But there is a 
great difference between the two in the matter of com- 
pressibility. Liquids are so little compressible that we are 
almost justified in speaking of them as Incompressible 
Fluids. Gases, on the other hand, re- 
spond so perfectly to every change of 
pressure that we may properly speak of 
them as Compressible Fluids. This dis- 
tinction will need to be kept in mind in 
our study of pressure in liquids and in 



105. The Mercury Pressure Gauge.— 
A very convenient instrument for the 
study of pressure in fluids is the mer- 
cury pressure gauge shown m Figs. 43 
and 44. In Fig. 43 a column of water, 
a b, is represented as being balanced by 
a column of alcohol, b c, both columns 
resting upon mercury in the part of the 
tube below b. In Fig. 44 the column of 
water, ab, is balanced by a column of 
mercury, b c. In both cases it is obvious that the mercury 
acts as a sort of scales for weighing. In Fig. 44 the col- 
umn of water, a b, has forced the mercury down to b in the 



c-% 

T a | 

I 3 

I s 

I I 

S i 

I 1 

1 I 

! I 



Fig. 43. 



U 



Fig. 44. 



90 PHYSICS 

left arm of the pressure gauge and up in the right arm 
until it supports a column of mercury, b c, equal in weight 
to itself. In Fig. 43 the column of water a b is equal in 
weight to the column of alcohol b c. 

106. Pressure in Terms of Inches of Mercury. — We may 
speak of the pressure in terms of inches of mercury. Thus 
the pressure of a column of water 13.6 inches long is about 
equal to a column of mercury one inch long ; half an inch 
of mercury would represent the pressure of a column of 
alcohol about eight and a half inches long. In inflating 
a football one is likely to exert a pressure of about three 
inches of mercury. The ordinary pressure upon a steam 
radiator is likely to be about ten inches of mercury. That 
is, if we connect one arm of a mercury pressure gauge with 
the inflated football or the steam radiator these pressures 
would force the mercury up in the other arm of the pres- 
sure gauge three inches in the first case and ten 
inches in the second case. 

107. Pressure in Terms of Pounds per Square 
Inch. — We usually speak of pressure in terms of 
pounds per square inch. In Fig. 45 the column of 
water ab is represented as having a cross-section 
of one square inch and a height of 13.6 inches. 
It is balanced by a column of mercury b c, which 
is a cubic inch in volume. Now, a cubic inch of 
mercury weighs about half a pound ; the 
weight of the column of water is, there- 
fore, about half a pound; the pressure 
upon the square inch of surface of mer- 
Fig. 45. cury where the water rests upon it is 

half a pound. It is manifest that if the 
cross-section of the tube were half as large there would 
be half the quantity of water, and half the weight — i. e., 
one quarter of a pound upon half a square inch; or if the 
tube were one quarter or one tenth as large in cross-section 
the weight of water would be one quarter or one tenth as 




PRESSURE IN LIQUIDS 



91 





much. The pressure would, however, in all cases be at the 
rate of one half pound to the square inch, so long as the 
height of the column remained 13.6 inches. And let the 
diameter of the column a b be never so small or great it will 
in every case balance the cubic inch of mercury b c, pro- 
vided its height remains 13.6 inches. 

108. First Princi- 
ple. — (a) Pressure in ) I r^^ 
liquids is proportional 
to the depth alone, and 
is not influenced by 
the size or shape of the 
vessels which contain 
them. (b) At any 
given depth the pres- 
sure is equal in all 
directions. 

The first part of 
this principle may be 
illustrated by such 
apparatus as is repre- 
sented in Fig. 46, and 
the second part is 
shown by such 
apparatus as is 
represented in 
Fig. 47; ab is 
in each case the 
depth of the 
water measured 
vertically, and 
be is in each 
case the mer- 
cury column 

sustained by the pressure of the liquid, 
found to be 13.6 as long as b c. 




Fig. 46. 




HI 



Fig. 47. 



In all cases a b is 



92 



PHYSICS 



D 



m 

b 



no <S> 




109. Pressure is due wholly to Gravity. — A few dia- 
grams, such as those represented in Fig. 48, may help one 
to feel that it is not unnatural that the pressure of gravity 

upon particles of matter free 
to move among themselves will 
result in pressure sidewise or 
even upward. Having no sin- 
gle point or even surface of sup- 
port, liquids do not, like solids, 
exert a downward force of mg 
(mass multiplied hy the accel- 
eration of gravity; sections 65 
and 69) on the bottom of the 
containing vessel. The pres- 
sure upon any point of surface 
depends not on the amount of 
liquid, but entirely upon the 
height of the liquid above the 
center of the unit surface. 
In Fig. 49 the vessels have all the same-sized bases, 
and the water stands at the same height in all. The 
amount of water in the several vessels is manifestly very 
different, but the pressure upon the base of each vessel is 
the same. This seems at first sight an evident paradox. 
The weight of water on the base A is manifestly the whole 
weight. But this is 
equal to the volume 
of the cylinder in 
cubic centimetres 
(since one cubic 
centimetre weighs 
one gram), and the 
volume is equal to 
the height multi- 
plied by the area of the base. By contracting the sides, 
as in B, the amount of water is greatly reduced, but the 



Fig. 48. 




Fig. 49. 



PRESSURE IN LIQUIDS 93 

pressure on the base remains the same. The pressure on 
the portion of the base a b is equal to a volume of water, 
h X ab. This has the same intensity per unit surface as 
in A, since the height, h, is the same. But we could not 
have a greater pressure on a b than at c and d, for in that 
case there would be a now of water toward c and d accom- 
panied by depression of the column which stands over a b 
and a reduced pressure on ab\ but we know from our ex- 
perience that no such flow does take place. The pressure 
on the base a b is transmitted equally in all directions, and 
acts downward at c and d with precisely the same force as 
it does on a b. In the vessel G there is more water than 
there is in A, but there is no increase of pressure on the 
base. 

110. Upward Pressure in Liquids. — Because liquids trans- 
mit pressure equally in all directions, it follows that at any 
depth the upward pressure due to the weight of the liquid 
must be exactly the same as the downward pressure. Con- 
sider the level a a in the tank of 
water shown in Fig. 50. The 
downward pressure on a square 
centimetre, b c, is the height of a 
column of water be X h. If this 
pressure were not counterbal- Fig. 50. 

ancecl there would be a downward 

movement of the liquid. But no such movement takes 
place. Every square centimetre on the level a a has the 
same downward pressure of h grams, and that pressure, 
being transmitted equally in all directions, acts upward on 
b c and just counterbalances the downward pressure. 

The upward pressure of liquids is illustrated by a simple 
experiment. An open glass cylinder (Fig. 51) with ground 
edges has one end closed by means of a thin ground-glass 
cover plate. In the air the plate has to be held up against 
the cylinder, but as soon as cylinder and plate are immersed 
to a depth of about one centimetre in water, the upward pres- 



94 



PHYSICS 



Fig. 51. 



sure of the water holds the plate against the cylinder. The 
deeper the cylinder is pushed the greater the upward pres- 
sure, and the more securely is the plate held against the 
cylinder. If now water be poured into the 
cylinder, the cover plate will fall when the 
water in the cylinder is nearly at the same 
level as the water outside in the tank. The 
difference in level represents the volume of 
water whose weight just equals that of the 
cover plate. Had the cylinder been filled with 
alcohol, or some liquid lighter than water, the level inside 
the cylinder would have to be considerably higher than 
the level outside to make the cover plate fall off. 

The upward pressure on the plate is equal to the weight 
of a column of water having the plate for its base, and a 
height equal to the distance from the surface to the lower 
face of the plate. The doivnward pressure is equal to the 
weight of the liquid inside the cylinder, plus the weight 
of the plate itself. 

This upward pres- 
sure of liquids is man- 
ifested when you raise 
the tubular stopper 
in a bath tub full of 
water. The water 
rushes up the tube by 
reason of the pressure 
of the surrounding 
water. 

111. Liquids 
seek their own 
Level. — If we have 

several communicating vessels, as shown in Fig. 52, and 
pour water into one of them, we notice immediately that the , 
water rises in all of them to the same level. We can not 
fill one vessel without filling all. On the whole, we should 




PRESSURE IN LIQUIDS 95 

expect this, for if we imagine for a moment that we have 
succeeded in filling one vessel without filling the others, 
and look at the pressures, we shall find an impossible state 
of affairs. The liquid in the first vessel will be unsupported 
at the outlet into the second vessel. With the second ves- 
sel empty, there will be nothing to balance that pressure 
and nothing to prevent the liquid from flowing out, which 
it accordingly does. The pressure is only balanced at each 
outlet when the liquid stands at the same height in each 
vessel. This is popularly exjoressed by saying that liquids 
seek their own level. Every free surface of water, unacted 
upon by wind or current, is perfectly level, and is perpen- 
dicular to the direction of gravity. Consider for a moment 
the force at work. The only force is gravity, and this al- 
ways acts vertically down- 
ward. If the surface were 
not level, but were inclined, 
as indicated in Fig. 53, we 
should have at a a downward 
pressure, represented by the 
arrow. This pressure is trans- 
mitted equally in all direc- 
tions, and consequently acts 

upward at b. In the absence of any corresponding down- 
ward pressure at h the water rises at #, and must sink at a, 
only coming to rest when in all parts of the liquid, the 
downward pressure and the upward pressure, are the same. 
AYe can sum this up by saying that the surface of liquids 
is always perpendicular to the direction of force acting 
upon them. Consequently the surface of a still pond or 
lake is always level, since it is everywhere perpendicular to 
gravity. In the case of the ocean or of large bodies of 
water generally, the direction of gravity changes about 1° 
every 69 miles, and consequently the surface, being per- 
pendicular to gravity, is always changing, and is in reality 
spherical. Of course, the surface of small ponds and lakes 



96 



PHYSICS 




is also strictly spherical, but in such small distances the 
departure from a strict plane is not noticeable. 

112. Buoyancy. — From what we have learned thus far we 
know that any object which sinks beneath the surface of a 
liquid will have pressure exerted upon it proportional to 
the depth which it sinks into the liquid, and due wholly to 
the weight of the liquid. Let us consider the forces act- 
ing upon a cubic centimetre of water, a, Fig. 54, in a tank 
of water. Let us suppose the upper surface of the cube a 
to be 1 centimetre below the surface of the 
water in the vessel. On the upper face of 
the cube there will be a downward pressure 
equal to 1 gram, the weight of the column 
of water above it. The horizontal pressure 
upon the four faces may be neglected, since 
they come from four directions at right 
angles and just balance one another. On 
the lower face of the cube there will be an 
upward pressure of 2 grams, equal to the 
weight of a column of water, whose height is 2 centimetres 
and whose cross-section is 1 square centimetre. The down- 
ward pressure of water upon the upper face of the cube is 
1 gram, and the upward pressure of water upon its lower 
face is 2 grams. But the cube does not move upward, be 
cause its own weight is 1 gram. All the forces are balanced, 
and the cube of water stands still. This would of course be 
true also of a cubic centimetre of any other substance which 
weighed exactly 1 gram. Let us substitute for the cube of 
water a cube of wood about half as heavy as water. The 
downward forces will be the weight of the wood and the 
weight of the column of water above it, equal to \\ grams. 
The upward force will be equal to 2 grams, as before. Hence 
there will be an unbalanced buoyant force of half a gram, 
and the wood will move upward until it reaches a place 
where the opposing forces are equal. Pursue this method 
of reasoning, and find out that it must rise until it displaces 



Fig. 54. 



PRESSURE IN LIQUIDS 97 

just its own weight of water — i. e., until only half of the 
cube is submerged. Had the cube been of cast iron, density 
7.2, supposing it to be in its original position, the upward 
pressure upon its lower face would be 2 grams, as before, 
and the downward pressure would be its own weight — 7.2 
grams plus the weight of the 1 centimetre of water above 
it, 1 gram, making a total downward force of 8.2 grams. 
Hence the cube would sink with a force of 8.2 — 2 = 6.2 
grams. Suppose the bottom of the vessel is 5 centimetres 
below the surface of the w T ater and the iron cube to be rest- 
ing upon it. What would be the buoyant force upon it, and 
with how much force would it press upon the bottom of the 
vessel ? If this cube of iron were suspended upon a string 
at various depths within the liquid, but always wholly sub- 
merged, would it in every case pull with the same force 
upon the string ? Would your answer be the same if liquids 
were compressible ? Balloons may be made to float higher 
or lower in the air by increasing or decreasing their weight. 
This is not possible with objects wholly submerged in 
liquids. It is a matter of daily experience that as soon as 
a floating object becomes heavy enough to sink beneath the 
surface of the water it goes straight to the bottom. The 
only way to prevent this would be to have liquids of dif- 
ferent densities, and which do not readily mix, arranged in 
layers one above the other. If a vessel is half full of wa- 
ter, density 1.00, and half full of ether, density .71, a block 
of oak, density .85, dropped into the vessel will sink to the 
bottom of the ether layer and float on the water under- 
neath. An egg will sink in fresh water and float in salt 
water. Consequently if a jar be half filled with salt water 
and then fresh water be carefully added, an egg dropped 
into the jar will sink halfway, and remain suspended at 
the meeting plane of the two liquids. From such investi- 
gations we may deduce the principle that a body wholly 
submerged in a liquid is buoyed up by a force exactly equal 
to the weight of its own volume of the liquid. 



98 



PHYSICS 



This is prettily illustrated by the apparatus represented 
in Fig. 55. The upper cylinder is hollow, the lower cylin- 
der solid, and has such a volume as to exactly fit inside of 
the upper cylinder. They are suspended as shown in the 
figure, and carefully balanced. Then water is poured into 
a vessel so as to submerge the lower cylinder. Its buoyant 




Pig. 55. — Principle of Archimedes. 



force lifts the left arm of the balance. The upper cylinder 
is then filled wi^h water, and this is found to restore the 
balance, showing that the buoyant force upon the sub- 
merged cylinder is exactly equal to the weight of its own 
volume of water. The same experiment may be performed 
less elaborately by weighing any solid of known volume, 
say n cubic centimetres, first in air and then in water. The 
loss of weight will be just n grams. 



PRESSURE IN LIQUIDS 



99 



Every boy who has lifted a stone under water knows 
how heavy it suddenly becomes when he tries to bring it 
above the surface. The transporting power of running 
water is greatly increased by the buoyancy of the water and 
the consequent loss of weight on the part of the material 
carried. 

We may make use of this principle to find the volume 
of an object. For example, if an object weighs 3 grams 
in air and 2 grams when 
wholly submerged in water, 
the buoyant force of the 
water is 1 gram — i. e., its vol- 
ume is 1 cubic centimetre. 

113. Specific Gravity.— It 
is obvious that the object 
mentioned in the last para- 
graph was three times as 
heavy as water. We express 
this by saying that its spe- 
cific gravity is 3. 

The balance may be used 
to determine the specific 
gravity of both solids and 
liquids. 

a. Solids. — A fine silk 
thread or wire is tied around 
the solid and a loop made of 
the end several inches away 
from the solid, so that the 
whole may be freely suspended from the arm of the bal- 
ance (Fig. 56). The weight is then taken in air. Let 
this be represented by x. A glass of water is now brought 
under the solid and raised until the entire solid is cov- 
ered by the water. The solid must, of course, swing freely 
in the water, and not touch the sides of the beaker. The 
weight is taken in water. Let it be represented by y. 




Fig. 56. — Specific-gravity balance. 



100 PHYSICS 

Then x — y will represent the loss of weight in water, and 

we will have -r. •, x 

specific gravity = 



y 

Example. — A piece of limestone rock. 

Weight in air = 17.65 

Weight in water = 10.99 

Loss of weight in water = 6.66 

Specific gravity = l ^ = 2.65. 

That is to say, limestone is nearly two and two thirds 
times as heavy as an equal volume of water. 

b. Liquids. — To determine the specific gravity of a 
liquid we must know the weight of a given volume of it, 
and also the weight of the same volume of water. The 
ratio of one to the other is the specific gravity. We can 
easily find these two quantities by taking a suitable glass 
plunger of known weight (x) and weighing it first in the 
liquid whose specific gravity is to be tested (y) and then in 
water (z). The loss of weight in each case will evidently 
be the weight of a volume of liquid equal to the volume of 

the plunger, and we shall have specific gravity = x ~$ . 

Example. — Alcohol. 

Weight of plunger in air = 10.21 grams (x) 

" " alcohol = 8.45 " (y) 

" water = 8.02 " - (z) 

a .„ ., 10.21-8.45 1.76 

Specific gravity = 1Q 21 _ 8 Q2 = ^ = .8 

We have two kinds of hydrometers for determining 
specific gravity, the hydrometer of constant volume and the 
hydrometer of constant weight. 

By the first we can determine the specific gravity of 
both solids and liquids. A form of the instrument, known 
as Nicholson's hydrometer, is shown in Fig. 57. 

The solid whose specific gravity is to be determined is 
placed on the upper scale pan and weights added until the 



PRESSURE IN LIQUIDS 



101 



hydrometer sinks to the index point. The solid is then 
placed in the lower pan under water and weights added to 
the upper scale until the buoyancy of the now submerged 
solid is compen- 
sated. The added 
weights represent 
the weight of the 
water displaced by 
the solid. This 
divided into the 
weight of the solid 
gives its specific 
gravity. In using 
the hydrometer for 
liquids it is simply 
floated in the 
liquid and 
then in pure 
water, and the 
weight of the 
hydrometer it- 
self, plus the added weights, will give the weights of the 
liquid and of the water displaced. One divided by the 
other is the specific gravity. 

The hydrometer of constant weight may be used only for 
liquids. It is made of glass, and consists of a cylinder or 
tube, terminating below in a bulb loaded with mercury or 
shot, and above in a long slender tube which carries a scale 
and projects above the surface when the hydrometer is 
floated in water (Fig. 58). 

Xow, in order that any solid may float, it must displace 
an amount of liquid whose weight is just equal to its own 
weight. Hence when the hydrometer is put into liquids 
lighter than water it sinks deeper, and when into liquids 
heavier than water it rises higher above the surface. If 
the point on the scale to which the hydrometer sinks in 




Fig. 57. 



-Hydrometer of constant weight. 
(Nicholson's.) 



102 



PHYSICS 



distilled water be marked 1, the markings on the scale 
below this point will be greater than 1, and above will be 
less than 1. 

By adjusting the hydrometer so that it will sink about 
midway on the scale in water, the one instrument may 
measure specific gravities greater and less than unity ; but 

in order to gain 
greater sensitive- 
ness it is common 
to use two instru- 
ments, one for liq- 
uids denser than 
water and the othei 
for liquids lighter 
than water. 

The alcohol- 
meter is a hydrom 
eter made especial- 
ly to measure alco 
hoi. The upper 
end of the scale, 
marked 100, is the 
point to which the 
instrument sinks 
in pure alcohol. 
The lower part of the scale, marked 0, is the point to which 
it sinks in distilled water. The intermediate readings give 
directly the percentage of alcohol. 

The lactometer is a hydrometer graduated with special 
reference to milk, and is used by official inspectors. Other 
hydrometers, such as Baume's, are graduated empirically — 
that is, without direct reference to specific gravity — and 
are used in industries where it is desired to keep trade 
secrets. 

In all of the above work it has been assumed that the 
solids are heavier than water and will not dissolve. In case 




Hydrometers of constant volume. 



PRESSURE IN LIQUIDS 103 

they are lighter they must be weighted with some solid of 
known specific gravity and the calculation made accord- 
ingly. In case they dissolve in water, another liquid in 
which they will not dissolve must be used and the neces- 
sary correction made. 

There is a classic story to the effect that Hiero, Tyrant 
of Syracuse, having a daintily wrought crown which he 
suspected not to be of pure gold, sent it to the philosopher 
Archimedes to test for him. The philosopher was puzzled, 
for the crown was to be tested without any damage to the 
clever workmanship. But one day, being in the bath and 
noticing that his body displaced its own volume of water, 
it occurred to him that buoyancy would enable him to de- 
termine the specific gravity of the crown, and thus he 
might compare it with pure gold. He sprang out of the 
water shouting, " Eureka ! " {I have found it.) He demon- 
strated that the crown was not gold, and Hiero had the 
fraudulent craftsman dreadfully punished. Archimedes 
is celebrated for his researches in buoyancy and specific 
gravity. 

114. The Specific Gravity of the Human Body. — There is 
a great difference in the density of the human body. In 
fat persons it is less and in thin persons more, but the gen- 
eral average may be stated at .89. All persons ought, 
therefore, to float; yet many drown each year by taking 
water into their lungs until the specific gravity rises above 
1. It is well known that the bodies of persons who have 
drowned float again a few days after death. This is due to 
the inflation of the bodies with gases produced by decom- 
position. 

There are salt lakes where the density of the water is 
so great that the human body can not sink. The Great 
Salt Lake in Utah is such a place, and also the Dead Sea in 
Palestine. 

115. How Iron Ships Float. — Modern ships are some- 
times built of iron or steel, specific gravity 7.75, but being 



104 PHYSICS 

hollow they displace, without sinking to a very great depth, 
an amount of water that easily equals their own weight. 
We sometimes hear that a certain ship is of 10,000 tons 
burden or displacement. This is the weight of the water 
which it displaces. This must be the buoyant force of the 
water and therefore the total weight of ship and cargo. 
One cubic foot of water weighs about 62.5 pounds. Ten 
thousand tons of water would fill a tank 400 feet long, 40 
feet wide, and 20 feet deep. These dimensions are not so 
great as some of our largest ocean steamers. By building 
the ship in water-tight compartments it is practically un- 
sinkable. In case of collision one or more compartments 
may be broken open and the ship settle considerably, but 
the displacement of the other compartments will still keep 
it afloat. 

116. Stability of Floating Bodies. — There are two points 
to be considered with reference to the stability of floating 
bodies. The center of gravity— that is, the point of appli- 
cation of the downward force — and the point of application 
of buoyancy — the upward force. This latter must be the 
center of mass of the submerged portion. The center of 
gravity and the center of buoyancy must always be in the 
same vertical line, for otherwise, the forces being equal and 
parallel, we should have a couple (see page 68), and rota- 
tion would bring the two forces into line. When the cen- 
ter of gravity is below the center of buoyancy and in its 
lowest possible position the equilibrium is stable. When 
the center of gravity is above the center of buoyancy or is 
not in its lowest possible position, the equilibrium is un- 
stable and the floating body will capsize if in doing so the 
center of gravity can assume a lower position. The danger 
in standing up in a canoe or other light boat is that in 
doing so the center of gravity of the system is lifted above 
the center of buoyancy. Yachts have keels of lead pro- 
jecting far down into the water so as to carry the center of 
gravity as far below the center of buoyancy as possible. 



CHAPTEK XV 

FRESSURE IN GASES 

117. General Behavior of Gases. — In their general me- 
chanical behavior, gases differ from liquids only in being 
sensibly compressible and infinitely expansible. They all' 
exert pressure because they all have weight. 

118. Second Principle. — (a) Pressure in gases increases 
with the depth, but is not proportional to it. (b) At any 
given depth the pressure is equal in all directions. 

119. The Atmosphere. — We speak of tumblers, pails, and 
other hollow vessels as being empty when they contain only 
air ; but a very little examination shows us that the air is a 
very real substance, and that we must take account of it 
quite as seriously as of brick and mortar. A tumbler turned 
upside down and thrust into water is not filled by the water, 
for the air is already there and excludes the water. 

For us the air is an ever-present reality, for we live at 
the bottom of an aerial ocean, which is estimated to be 
more than two hundred miles deep. Those of us who live 
at the sea level are at the bottom of this ocean, where the 
pressure is greatest. Those who live at places like Denver 
(about five thousand feet high) or Leadville (about ten 
thousand feet) are less deep in this ocean of air, and are 
under considerably less pressure than we are. Men, ani- 
mals, and plants are no doubt affected to some extent by 
the variation in atmospheric pressure at different heights 
upon the earth's surface. It will not do to forget the 
atmosphere, or leave it out of the count, whether we are 

105 



106 PHYSICS 

dealing with energy and matter, or with animals and plants. 
It is an ever-present and ever-variable fact. 

120. Weight of Air. — " Light as air " used to mean light 
as nothing. Aristotle, the encyclopaedia of the ancient 
world, had hinted that air might have weight ; but in gen- 
eral to the early philosophers air and space were about the 
same thing. Galileo and Guericke showed that air, like all 
matter, has appreciable weight. If a glass globe holding 
1 litre, 1,000 cubic centimetres, be exhausted of air and 
weighed, then refilled with air and weighed, the difference 
in weight, if the experiment be made at the sea level and 
at the temperature of freezing water, will be found to be 
1.293 grams. This represents the weight of 1 litre of dry 
air under normal conditions. Hence 1 centimetre of air 
weighs .001293 gram, and this number represents the den- 
sity of air (page 43). The density of water is 773 times as 
great. In the same way we may find the weight of one 
litre of hydrogen, .089 gram, or of one litre of oxygen, 1.429 
grams, or of one litre of any other gas. These numbers 
divided by 1,000 will give the density of the gas. It is 
more common to speak of their specific gravity, however. 
This is their density divided by the density of air. 

001 9Q3 = '° 69 = s P ec ^ c g ravr ty of hydrogen. 

.001429 K 

001293 = 1-1056 = specific gravity of oxygen. 

Or, knowing the weight of one litre of dry air, and the spe- 
cific gravity of a gas, we can readily calculate the weight of 
one litre of the gas. 

Thus : 1.293 gr. X sp. gr. of gas = wt. of 1 litre of the gas. 
1.293 gr. X .069 = .089 = wt. of 1 litre of hydrogen. 

A cubic foot of air weighs about 1.28 ounces. Thus, the 
air in a lecture-room 40 X 50 X 25 feet weighs about two 
tons. Imagine the air of such a lecture-room moving across 
the country at the rate of seventy-five miles an hour, as it 



PRESSURE IN GASES 



107 



might in a hurricane. It is easy to conceive that two tons 
of air moving at such velocity might dislodge some build- 
ing, or uproot some trees, or pile up sand or snow or sea, 
or drive furiously a heavy sailing vessel ; and the fact that 
it moves with such momentum impresses us not only that 
it has velocity but also weight. 

121. The Barometer. — Over two hundred and fifty years 
ago (1613) Torricelli, a pupil of Galileo, conceived a plan 
for measuring the pressure of the 
atmosphere so simple and direct and 
so altogether excellent that it has 
been used ever since. A straight glass 
tube (Fig. 59), about one metre long 
and about five millimetres in diam- 
eter, is closed at one end and com- 
pletely filled with mercury. The open 
end is then closed by the thumb, and 
the tube inverted. It is thrust 
J under the surface of a bath of 
mercury and the thumb with- 
drawn, as soon as all com- 
munication with the air is 
closed off. The mercury in 
the tube falls a little, 
and after a few oscilla- 
tions comes to rest at a 
point many centimetres 
above the level of mer- 
cury in the bath. We Fig. 59. 
Hi represent this height 

U by h. At the sea level, under usual conditions of 
Fig. 60. weather, and at the freezing point, it is seven 
hundred and sixty millimetres. The simple form, 
represented in Fig. 60, is much in use. Such an instru- 
ment is known as a barometer (pressure gauge). Let us 
consider the forces at work. On the free surface of the 




108 PHYSICS 

mercury there is manifestly the downward pressure of the 
atmosphere. This is transmitted, and acts upward in the 
tube at the same level with undiminished intensity. Here 
it meets a downward force, the weight of a column of mer- 
cury of height h. As the mercury in the tube stands still, 
the two forces must be equal. As h would be the same, 
whatever the cross-section of the tube, let us consider it to 
be 1 sq. cm. The weight of a column of mercury 76 cm. 
high and 1 sq. cm. in cross-section is manifestly the weight 
of 76 cubic cm. of mercury. As the density of mercury is 
13.596, the weight of 76 cubic cm. must be 76 X 13.596 = 
1033.296 grams. This, then, is the pressure exerted by the 
atmosphere on every square centimetre of surface, and is 
commonly called one atmosphere. 

The pressure of the atmosphere is thus expressed as 
weight. It may be expressed as force by multiplying the 
result by g, since F = ma = mg. 1033.296 X 980 = 1,012,630 
dynes (pages 52 and 55). 

The barometer is like a pair of weighing balances where 
liquid pressure upon one scale-pan counterbalances gaseous 
pressure upon the other scale-pan. 

In English units h, under normal conditions, is about 
thirty inches. If we consider the barometer to have a 
cross-section of one square inch, the atmospheric pressure 
per square inch must be the weight of thirty cubic inches 
of mercury, or 14.7 pounds. Hence, it is common to say 
that the atmospheric pressure is fifteen pounds to the 
square inch. In one convenient form of barometer, For- 
tin's (Fig. 61), the cistern has a flexible bottom, and a little 
ivory pointer establishes the level of the mercury. A 
screw in the lower part of the cistern makes it possible to 
raise and lower the flexible bottom, and so adjust the level 
of the mercury to the pointer. This forms the zero of the 
permanent scale. By means of the sliding vernier at the 
top of the barometer tube (Fig. 62) the reading may be 
taken directly and with great accuracy. 



PRESSURE IN GASES 



109 




Other liquids may be used in a barometer. The special 
advantage of mercury is that its great density makes the 
column conveniently short. Its disadvantage is that the 
variations in h are correspondingly 
small. In a water barometer we have 
the reverse conditions, an inconvenient- 
ly long column, 76 cm. X 13.596 = 
1033.296 cm., and large variations in h. 
122. The Aneroid Barometer. — The 
mercury barometer is the most accu- 
rate form that we can have. It is, 
however, not conveniently portable, 
and where observations are to be made 
on top of a high mountain or other 
spot of difficult access, the aneroid 
barometer is often substi- 
tuted. In this the atmos- 
phere acts against the flex- 
ible corrugated metal cover 
of a sealed box (Fig. 63). 
The greater the pressure, 
the more the flexible cover 
will be forced in. Its mo- 
tion is transmitted by a 
system of delicate levers 
to a light pointer, which 
moves over the surface of 
a graduated circle. The 
reading is made directly 
in millimetres of mercury, 
the graduation being effect- 
ed by comparison with a *venderT 
standard barometer. 
123. Variations in Atmospheric Pressure.— The pressure 
of the atmosphere is always changing. The barometer 
records this change, and serves us in a double capacity. If 





Fig. 61.— Fortin's 
barometer. 



110 



PHYSICS 




the barometer be fixed, it records the change at any one 
spot; if the barometer be taken to different elevations 

above the sea, it tells us 
the elevation by means 
of the change. 

First. If the ocean 
of air covering the earth 
were allowed to come 
to rest we should have 
final equilibrium, when 
the pressure was exact- 
ly the same at the same 
altitude all over the 
world. In that case, a 
fixed barometer would 
always give the same 
reading, and, once 
taken, the barometer 
would be of no further 
But we all know that the air is far from being at 
rest. It is almost constantly in motion. The rotation of 
the earth and the difference of temperature set up cur- 
rents and counter-currents in this aerial ocean that give us 
all the phenomena of wind, from gentlest zephyr to fiercest 
hurricane. But the effort at equilibrium goes on just the 
same, and the barometer has much to say about our prob- 
able weather. 

A low barometer indicates storm, because it means 
that air from surrounding regions will rush in to restore 
equilibrium, and will probably cause precipitation — rain, 
snow, hail, sleet — according to the season. A high or rising 
barometer means fair weather, because it indicates a flowing 
away of air from that spot, and consequently freedom from 
outside influence. 

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grams from all the signal stations throughout the country 



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112 PHYSICS 

stating the barometer and other climatic conditions. These 
data are at once put down on the map so that one can see 
the conditions over the whole country at a glance. Lines 
joining places of the same pressure are called isobars. 
These lines are found to curve about certain centers. The 
accompanying weather map (Fig. 64) illustrates the actual 
conditions of the atmosphere with respect to pressure in all 
parts of the United States on a certain day and hour. 

Secondly. The variations in pressure at any one spot 
are small compared with its variations when taken to differ- 
ent heights. If the atmosphere were of uniform density 
throughout, like an ocean of water, it would be about five 
miles high and the elevations in it would be directly pro- 
portional to pressure ; but on account of its compressibility 
and variations in the temperature the density of the atmos- 
phere is very far from uniform, and a somewhat compli- 
cated formula must be used to get the exact height. The 
atmosphere is naturally much denser near the surface of 
the earth, since it is here under greater pressure. Half the 
atmosphere is within three and a half miles of the earth, 
since at that elevation, about 5^ kilometres, the barometer 
stands at 38 centimetres. For moderate altitudes the fall 
of h is about 1 centimetre for an ascent of 100 metres. 

124. Boyle's Law. — On account of the perfect compressi- 
bility and elasticity of gases their volume changes with the 
least change of pressure. Boyle in England and Mariotte 
on the Continent found that the volume of a gas is in- 
versely proportional to the pressure it supports, or, in other 
words, that the product of pressure and volume, p v, is 
always constant. 

p v — p' v' —p" v." 

This can readily be shown experimentally. For pres- 
sures greater than one atmosphere, Figs. 65 and 66 represent 
convenient forms of apparatus. The latter consists of two 
short pieces of glass tubing connected by rubber tubing. 
The lower piece of glass tubing is closed at c. Mercury fills 



PRESSURE IN GASES 



113 




- 



the tubing from a to b. The arm a is lowered until the 
mercury stands at the same level in both arms. The length 
of the column of air b c is then noted while 
it is under the pressure of the atmosphere 
alone. The arm a is then raised until the 
mercury at a is, say, thirty inches higher 
than at b. The air b c is then under the 
pressure of two atmospheres, and it will be 
found to have contracted to one half its 
original volume. If the difference in level 
between a and b is made fifteen inches, the 
pressure will be three halves of an atmos- 
phere and air will be compressed to two 
thirds its original volume. If the pressure 
is made four thirds of an 
atmosphere, the volume 
will be reduced to three 
fourths, etc. 

For pressure less than 
an atmosphere, Fig. 67 rep- 
resents the way the appara- 
tus is used. Suppose a is 
fifteen inches below b, then 
the pressure upon the air 
b c is one atmosphere minus 
half an atmosphere — i. e., 
the pressure is reduced to 
one half and the volume 
will be increased to 2. If 
a is made twenty inches be- 
Fig. 66. Fig. 67. low b, the pressure will be 
one third and volume 3, etc. 
This is Boyle's law, which may be stated in words as 
follows : If the temperature be constant, the volume of a 
body of gas varies inversely as the pressure. The law is not 
absolutely correct, the variation being greatest in case of 
9 




Fig. 65. 



114 



PHYSICS 




those gases like ammonia and carbon dioxide that are easily 
liquefied. 

125. Closed Pressure Gauges. — For many purposes it is 
desirable to measure the pressure of a gas, as the pressure of 

steam in a boiler, the pressure of illumi- 
nating gas in a main, the pressure of air 
in the air blast of a furnace, and the like. 
If the pressure is but slightly in excess of 
one atmosphere the pressure gauge may 
be open. The reading is generally given 
directly in millimetres of mercury. For 
larger pressures the closed pressure gauge 
is more convenient (Fig. 68). The pres- 
sure is measured by the decrease in the 
volume of the inclosed air. Such an in- 
strument is practically a balance— on one side the elasticity 
of the air, on the other side the pressure of the gas. 

126. Buoyancy of Air. — It has already been stated that 
bodies immersed in any fluid, whether liquid or gas, are 
pressed upward with a 
force just equal to the 
weight of the fluid dis- 
placed. In the case of 
air, if the bodies are 
heavy, the buoyancy is so 
slight that it is common- 
ly neglected ; but in very 
accurate weighing the 
weight of an equal vol- 
ume of air must always 
be added to the apparent 
weight of a body, since its 

real weight is reduced by just that amount. True weight 
is therefore the equivalent of weighing in a vacuum. This 
buoyancy can be shown experimentally by a balanced hol- 
low sphere (Fig. 69). When it is placed under the receiver 




Fig 



PRESSURE IN GASES 115 

of an air pump and the air exhausted, the sphere shows 
itself to be heavier than its counterpoise. 

127. Balloons. — The principle of aerial buoyancy also 
makes it possible for us to construct air ships and balloons 
that will float and even remain at varying heights at our 
will. If we know the dimensions of a balloon and the gas 
with which it is filled, we can easily calculate its buoyant 
force. 

Example. — What weight will a spherical balloon 20 
metres in diameter and filled with hydrogen gas support at 
sea level ? Let the conditions be normal. 

Volume = \ ttD 3 = \ X 3.1416 X (2,000) 3 = 

4,188,800,000 cubic centimetres or 4,188,800 litres. 

Weight of 1 litre of air = 1.293 grams. 

Weight of 1. litre of hydrogen = .089 grams. 

Buoyant force of air upon 1 litre of H = 1.204 grams. 

Buoyant force of the air upon the balloon = 
4,188,800X1.204 = 5,043,315 grams. 
= 5,043.3 kilograms (about 5-J- tons). 
To find the available uplift we must, of course, subtract the 
weight of the silk envelope, cordage, car, and other para- 
phernalia. Those who know how to make H, and how to 
calculate quantities in chemistry by means of atomic 
weights, can readily calculate how much Zn would have 
to be dissolved in acid in order to fill such a balloon. 

Volume of balloon = 4,188,800 litres. 

Weight of 1 litre of H = .089 grams. 

Weight of total H = 4,188,800 X .089 = 252,802.2 grams. 
Xow for the chemical part : Zn + H 2 S0 4 = ZnS0 4 -f 2H. 
Each atom of Zn dissolved liberates 2 atoms of H, and 65 
grams of Zn will yield 2 grams of H, and hence 32| times 
252,803.2 grams of Zn will be required, or 4,108 kilograms 
(about 4^ tons). Thus the original question might take 
this form : How much Zn must be dissolved in acid in 
order to produce enough H to fill a balloon that is to have 
a buoyant force of 1,000 kilograms ? 



116 PHYSIOS 

It follows from the fact that the air is compressible, that 
the balloon, if its volume were constant, would displace a 
greater weight of air at sea level than at an elevation. If 
we desire the balloon to float near the earth's surface we 
may load it with bags of sand, and if we desire it to rise to 
greater heights we throw out these bags of sand. When 
we desire the balloon to descend we open a valve and let 
out some of the gas with which it is inflated, thus decreas- 
ing its displacement. 

Problems. — 1. What will be the weight of one litre of carbonic- 
acid gas, the specific gravity being 1.53 ? 

2. Which is absolutely the heavier, a pound of feathers or a 
pound of gold, and why ? 

3. If a body of gas occupy 1.2 litres, when h = 760 millimetres, 
what will be its volume when h = 748 millimetres ? 

4. A steel cylinder 3 feet high and 16 inches in diameter is rilled 
with oxygen gas. The pressure gauge shows that the gas has a 
tension of 240 pounds per square inch. How much space would 
this gas occupy if allowed to escape into the atmosphere under nor- 
mal conditions ? 



CHAPTEE XVI 

TRANSMISSION OF PRESSURE IN FLUIDS 

128. The Transmission of Pressure. — Chapter XIV dealt 
with pressure in liquids, and Chapter XV with pressure in 
gases. It must not be overlooked that the study of pres- 
sure in gases was to a large extent a review or reiteration 
of the first principle stated in section 108. Gases are 
separated from liquids in this discussion because they are 
compressible, while liquids are not. The third principle, 
which we are about to take up in this chapter, is equally 
applicable to both liquids and gases, and is merely a more 
extended discussion of what was first presented in sec- 
tion 109. 

When pressure is exerted on a rigid solid the pressure 
is transmitted in a straight line from the point of applica- 
tion of the pressure to the point of support of the solid. 
This is very obvious. When pressure is exerted on a fluid 
precisely the same thing takes place, but — and this is the 
important matter — where is the point of application of the 
pressure on a fluid, and where is the point of support of 
the fluid ? If we can answer these two questions we shall 
have the main facts about the mechanics of fluids. 

First, as to the point of application. This can not be a 
point at all, since a point would simply penetrate the fluid 
by pushing its molecules aside, and would exert no pressure 
whatever. Xo pressure can be exerted on a fluid except by 
an extended surface, and only then if the surface be moved 
against the fluid so rapidly that the fluid has no chance to 

117 



118 PHYSICS 

push by and escape, or by having the surface act against 
the fluid in a fluid-tight vessel. The first method is used 
in the blade of an oar, paddle wheel, propeller screw, or 
rudder, where pressure is exerted against water. In a 
windmill the same method is applied to the air. Observe 
that it makes no difference whether the surface is forced 
against the fluid, as in oar and paddle, or the fluid is forced 
against the surface, as in rudder and windmill. The sec- 
ond method of getting hold is well illustrated by the pres- 
sure of the piston upon the confined air in a bicycle pump. 

129. Third Principle. — Pressure exerted upon a fluid 
{liquid or gas) inclosed in a vessel is transmitted equally in 
all directions, the total pressure upon the walls of the vessel 
being proportional to the area. 

A person applies his mouth to one arm of the mercury 
pressure gauge and finds that he is capable of exerting 
with the air from his lungs a pressure sufficient to support 
a column of mercury three inches high — a pressure which 
we have learned (section 107) to designate as one and a 
half pounds pressure per square inch; if he now applies 
his mouth to two pressure gauges at the same time with 
an effort equal to that used before, he may make each of 
them register three inches, or one and a half pounds per 
square inch. In the same manner he may exert pressure 
upon any number of pressure gauges simultaneously, and 
find that it is as easy to hold up a hundred columns of mer- 
cury as it is to hold up one. There should be no paradoxes 
in physics. The statement of this third principle has been 
withheld until now in order that its truth should appear 
axiomatic rather than paradoxical. Should any one find 
this principle obscure he is advised to review Chapters XIV 
and XV. 

If a certain definite pressure is exerted upon a gas in- 
closed in a vessel, one, two, or any number of pressure 
gauges may be inserted in top, bottom, and sides of that 
vessel and all will be found to indicate the same pressure. 



TRANSMISSION OF PRESSUEE IN FLUIDS 



119 




Fig. 70. 



If the fluid had appreciable weight, as would be the case 
with a liquid, the pressure gauge would, of course, iudicate 
that iu addition to the given external pressure, and they 
would vary according to the depth of the liquid. 

Suppose rubber cloth is tied air-tight over the top of a 
jelly-cake tin (Fig. 70), the diameter of which is ten inches. 
A tube is inserted air-tight into 
the side of the tin ; a board is 
laid on top, and a weight placed 
upon it. A person who applies 
his mouth to the tube and exerts 

a pressure from his lungs of one and a half pounds per 
square inch may have the novel experience of lifting about 
118 pounds by the breath of his mouth. It is, of course, 
understood that the weight is to be only just started to 
rise, and not lifted any appreciable distance, in which case 
the tension of the rubber cloth may be neglected. 

The applications of the principles of fluid pressure in 
practical life are very numerous and important. They may 
be analyzed in the same way as machines (section 98). 
Power put in, minus friction = work got out 

pd = w s. 
130. Hydrostatic Press. — This depends upon Pascal's prin- 
ciple that fluids transmit pressure equally in all directions, 

and was one of the first and most 
famous applications of that prin- 
ciple. If a pressure of 100 kilo- 
grams be exerted upon a small 
piston (Fig. 71) having a cross- 
section of 1 square centimetre, 
and if the large piston P have a 
cross-section of 80 square centi- 
metres, it is clear that the up- 
ward pressure exerted on P will 
be 80 x 100 = 8,000 kilograms. 
Fig. 71. The hydrostatic press gives us a 





120 PHYSICS 

means of exerting enormous pressures with comparatively 
small forces. It must be remembered, however, that the 
principle of work comes in — that is, virtual velocities, 
pd = ws, and that what we gain in force we lose in space. 
In the present example P exerts a pressure eighty times as 
great as the pressure acting on p, but it only moves through 
one eightieth of the distance that p does. The press is 
used in some form in nearly every large engineering and 
industrial operation. It is also used to compress cotton, 
hay, and other substances, to extract the oil from seed, and 
to perform many other useful and Herculean labors. 



CHAPTER XVII 



APPLICATIONS OF PRINCIPLES OF FLUID PRESSURE 



131. The Density of Milk. — Cream is lighter than milk ; 
for this reason it floats npon the top of the milk. Skimmed 
milk is therefore heavier than whole milk, and it is evident 
that whole milk coming from different 

cows, and from the same cow at differ- 
ent times, must differ in specific grav- 
ity as the proportion of cream varies. 
The lactometer is an instrument for 
determining approximately the amount 
of cream in the milk by taking its spe- 
cific gravity, which in fairly good milk 
ought to he about 1.032. It will be 
noticed that water is also lighter than 
milk, so that it is possible for the milk- 
man to rob the cream from the milk 
and then restore it to its proper spe- 
cific gravity by adding water. This 
fraud must be detected by the intelli- 
gence of the customer acting together 
with the lactometer. 

132. The Bottle Imp, or Cartesian 
Diver. — Many historic pieces of appa- 
ratus which were for years the idols 
of physical museums, but which have 

rather fallen into disfavor because they served no better 
purpose than to mystify pupils, may be made interesting 

121 




Fig. 72. 



122 



PHYSICS 




Fig. 73. 



and properly instructive when used as a means of corre- 
lating principles which are thoroughly understood. The 
bottle imp, or Cartesian diver (Fig. 72), always has an air 
chamber, sometimes concealed, within the body. This cham- 
ber contains just enough air to float the ob- 
ject. The chamber communicates with the 
water outside by a very narrow passage. If 
any extra pressure is exerted upon the water 
some of it is forced into the chamber con- 
densing the air. The buoyant force is thus 
decreased and the object sinks. When the 
pressure is removed the air expands again, 
and the object rises. 

133. Magdeburg Hemispheres. — The pres- 
sure of the air is strikingly illustrated by 
the apparatus (Fig. 73) invented by Otto 
von Guericke, burgomaster of Magdeburg. 
The hemispheres should be made to fit to- 
gether air-tight by smearing vaseline around the edges. 
Ordinarily they separate with perfect ease, but when the 
air has been exhausted from within they are held together 
by a pressure of fifteen pounds per square inch ; and if 
their diameter is about four inches it will require a pull 
of nearly two hundred pounds to separate them. 

134. The Relation of Tension and Pressure. — It is helpful 
to think of the air in a bottle as a coiled spring (Fig. 74). 
If a weight of fifteen pounds rests upon the spring its ten- 
sion is fifteen pounds. By 
this we mean the force 
with which it tends to ex- 
pand. If now the weight 
be reduced to ten pounds 
the spring will expand un- 
til its tension is ten pounds. 
If the weight be reduced 
to five pounds the spring Fig. 74. 




PRINCIPLES OF FLUID PRESSURE 123 

will expand until its tension is only five pounds, etc. The 
tension must always equal the pressure in order that there 
may be equilibrium. The air acts like this spring, but it dif- 
fers in that it is indefinitely expansible. We may think of air 
in a bottle as being condensed in there under a pressure of 
fifteen pounds per square inch. Its tension or outward push 
upon the walls of the bottle is thus fifteen pounds per square 
inch. If the pressure be reduced, one half the air will ex- 
pand until half of it has been pushed out of the bottle. 
(See Boyle's Law, 124.) Its tension will then be only seven 
and a half pounds per square inch, etc. 

135. Bacchus Illustration.— This relation of tension and 
pressure is nicely illustrated by the apparatus which used 
to be called Bacchus illustration (Fig. 75). The tension of 
the air in the upper part of the bottle is, say, fifteen 
pounds per square inch. This would push the 
water out of the curved tube if the atmospheric 
pressure from without did not balance it. If now 
we place this bottle under a receiver and reduce j^~7 5 
the atmospheric pressure, or if it were carried up 

in a balloon into reduced atmospheric pressure, the tension 
of the air within would drive out a stream of water. If by 
any means the tension of the air within is reduced, or the 
pressure of the air outside is increased, water passes into 
the bottle. 

136. "Siphon" Bottles, Fire Extinguishers, Compressed- 
air Motors, and Explosives. — It is manifest that the so- 
called " siphon " bottles depend upon gas compressed 
within so as to have a much greater tension than fifteen 
pounds per square inch to drive out the liquid. This gas 
is carbon dioxide, and the pressure is frequently 140 
pounds per square inch. Many kinds of fire extinguishers 
illustrate this same principle. Some depend upon air com- 
pressed within them to throw the liquid upon the fire. 
Ammonium carbonate dissolved in water makes a very 
good liquid for this purpose. Others depend upon carbon- 




124 PHYSICS 

dioxide gas generated at the right moment within the 
apparatus to supply the tension which shall throw this 
stream. 

Air guns and all the various forms of compressed-air 
motors operate by the difference between the tension of the 
air from within and the pressure of the air from without. 
For example, if a cylinder with the capacity of two cubic 
feet has forty cubic feet of air compressed within it, its ten- 
sion, according to Boyle's Law, will be 300 pounds per 
square inch. This operating against an atmospheric pres- 
sure of fifteen pounds per square inch would give a working 
force of 285 pounds per square inch. 

All guns operate by the same principle as air guns — that 
is, the force ' which projects the bullet is the tension of 
greatly compressed gases. The explosives used generate a 
large volume of gases in a confined space. 

137. Diving Bells and Caissons. — Diving bells have a ten- 
sion of air within equal to the pressure of both water and 
atmosphere from without. The same principle is illustrated 
in the use of caissons for laying foundations under water. 
Tunnels are built through the mud under rivers, the work- 
men operating through holes in a huge steel cylinder, the 
tension of the air within being made sufficiently great to 
balance the pressure of mud, water, and atmosphere from 
without. This balance was so nicely adjusted in the work 
on the Hudson Eiver Tunnel that the tension of the air 
within was continually changed to correspond with the 
varying water pressure due to the rise and fall of the tide 
in the river. 

138. The Eardrum.— The inner chamber of the ear, like 
all other cavities of the body, is filled with air, or gases, 
having a tension equal to atmospheric pressure. In order 
that the membrane which is stretched across the tube be 
free from stress, the volume of the inside air must remain 
constant, and this can be done only by having its tension 
vary according to changes of atmospheric pressure. This 



PRINCIPLES OF FLUID PRESSURE 125 

is accomplished by the Eustachian tube, which communi- 
cates between the throat and the inner chamber of the ear. 
When atmospheric pressure increases, air is forced in 
through this fleshy tube until the tension within equals 
the pressure from without. "When atmospheric pressure 
decreases, air passes out by the same channel. " A cold in 
the head " sometimes clogs this channel ; then we experi- 
ence disagreeable sensations about the ears, caused by the 
sagging in or bulging out of the membrane of the ear, due 
to inequality between the tension within and atmospheric 
pressure without. 

Persons who are about to pass into a caisson are advised 
to try to force air out of their lungs while holding the nose 
and mouth closed. Why? Try it under ordinary atmos- 
pheric conditions, and explain the physical cause of the 
peculiar sensation in the ear. Persons about to come out of 
a caisson are advised to close the mouth and hold the nose 
shut, and perform the act of swallowing. Why ? Try this 
also under ordinary atmospheric conditions, and explain 
the physical cause of the peculiar sensation in the ear. It 
will be a more striking experiment if you swallow a mouth- 
ful of water or of food. Did you ever have a similar sensa- 
tion during eating, while suffering from a "cold in the 
head"? 

139. The Physics of Respiration. — A similar adjustment 
of tension to pressure is made in the act of breathing. By 
the contraction of certain muscles we are able to force the 
ribs upward and outward, and to depress the diaphragm. 
This enlargement of the chest cavity would produce a 
reduced tension of the gases within, if atmospheric pres- 
sure did not maintain the balance by pushing more air 
in, and thus inflating the lungs. By the contraction of 
certain other muscles we are able to contract the chest 
cavity. This would result in increased tension of the gases 
within, if they did not flow out at a rate to maintain the 
balance. 



126 



PHYSICS 



140. How Atmospheric Pressure upon the Human Body is 
sustained. — From this discussion it is manifest that the 
story is only half told when one speaks of the enormous 
pressure of thousands of pounds which the atmosphere 
exerts upon the human body. The other half, which 
should be coupled with this statement, is that all the tis- 
sues of the body are permeated by gases which have a ten- 
sion exactly equal and opposite to the atmospheric pressure; 

and that while the communica- 
tion between all bodily cavities 
is not as free as in the cases of 
lungs and eardrum, there is a 
somewhat slower communica- 
tion by the process of osmose, by 
which the balance between ten- 
sion from within and pressure 
from without is always main- 
tained. As might be expected, 
sudden and great changes in 
pressure, as one who goes up in 
a balloon experiences, occasion 
painful sensations before the in- 
ternal tension has had time to 
adjust itself. The tissues of the 
body in ordinary circumstances 
are under no more stress from 
atmospheric pressure than a very 
thin glass flask or a delicate tis- 
sue-paper bag whose mouths are open. Manifestly these 
are not enduring great stress from atmospheric pressure. 

141. "The Fountain in Vacuo."— The apparatus illus- 
trated in Fig. 76 shows again the relation of tension and 
pressure. If the tension of the air or any other gas inside 
the bottle be reduced by the action of a pump, or the 
contraction of the gas by cold, or the absorption of some 
of the gas by a substance introduced for that purpose, at- 




Fig. 76. 



PRINCIPLES OP FLUID PRESSURE 



127 



mospheric pressure from without will force the water in 
the lower vessel to rise until the volume of the gas inside 
shall be reduced so that its tension may equal the pressure 
upon it. Manifestly the water which 
enters the bottle is very nearly a meas- 
ure of the amount of air removed. 

142. Pumps. — It goes without say- 
ing that pumps have to deal with both 
classes of fluids — liquids and gases. 
We may take water pumps and air 
pumps as the two types. Both involve 
the same principle, but there are dif- 
ferences in form and construction that 
deserve notice. The most common 
form of water pump is the so-called 
cucumber pump, in which the pipe 
leading down into the well is simply a 
hollow length of cucumber wood. The 
rod attached to the pump handle has 
a piston at its lower end provided with 
a valve (a) opening upward (Fig. 77). 
At a given point somewhat below the 
lowest possible position of the moving 
piston, there is a valve (b) also capable 
of opening in an upward direction 
only. The valves are the essential 
part about such a pump. The action 
is very simple. \\ hen the pump is at rest, both valves a 
and b are closed by their own weight. Imagine a down- 
stroke of the pump rod. The chamber A is filled with air, 
which opens the valve a and escapes. Now picture an up- 
stroke. The valve a closes, and as the piston rises, increas- 
ing the volume of the space in the chamber between the 
two valves, the tension of the air in this chamber is reduced. 
Atmospheric pressure, being no longer balanced, presses to 
enter. The only entrance into the chamber from without 




Fig. 77. 



Cucumber pump. 



128 



PHYSICS 



is by the lower gateway b, and if the lower end of the pump 
tube dips into water the air will drive the water before it 
so long as its weight is less than the pressure to be exerted 
by the air. When enough air from the lower tube has been 
pushed up through b to make the tension in the chamber 
equal to the atmospheric pressure, minus the pressure of 
the column of water which now stands part way up the 
lower tube, equilibrium is again restored. The next down- 
and up-strokes repeat the operation until all the air in B is 
exhausted, and water begins to pass through the valves. 
The water that passes a is lifted bodily by the upgoing 
piston and escapes from the spout. It is plain that B must 
not exceed about thirty feet in length, or the pressure of 
the atmosphere will not support the column of water, and 
all our pumping would be in vain. 

These cucumber pumps are used in every village and on 
nearly every farm. The pump has many other forms, but 
the principle remains the same. The pump is frequently 
made of iron, and in large operations is run by steam. 

143. " Force " Pump. — The water thrown out by such a 
pump as has been described above falls in intermittent 

streams. The more rap- 
idly the pump is oper- 
ated, the less noticeable 
the inequality of the 
stream. It is possible, 
however, to slightly al- 
ter the construction of 
the pump, and make the 
stream of water reason- 
ably constant. This is 
accomplished in the so- 
called force pump (Fig. 
78). As before, there are two valves; one (b) opening up- 
ward into the chamber below the piston, and the other (a) 
opening out of the chamber into the delivery pipe. This 




Force pump. 



PRINCIPLES OF FLUID PRESSURE 



129 



latter pipe does not, however, simply terminate" in a spont. 
It lias connected with it an air chamber. Picture an up- 
stroke : b opens and water rushes up into the chamber below 
the piston. Now, a down-stroke : b closes and a opens. 




Double-acting pump. 



Water passes to the air chamber, and thence out of the 
delivery tube. The end of the delivery tube is constricted 
by a nozzle. This offers resistance to the flow of the liquid, 
and as a result the air in the air chamber is compressed, 
and continues to force water out of the delivery tube dur- 
ing the next up-stroke of the piston rod. The next down- 
stroke again opens a and forces water into the air chamber 
and into the delivery tube beyond. This secures a continu- 
ous and fairly constant stream of water. 

Double Pumps. — It is usual in the steam pumps to have 
the piston double-acting. In this case the piston is com- 




Fig. 79a.— Typical valves. 

monly horizontal, as shown in Fig. 79, and at each stroke 
of the piston water is drawn into one end of the piston 
10 



130 



PHYSICS 



chamber and forced out at the other end. In this way the 
stream of water is continuous. 

144. Air Pumps. — The air pump serves a double purpose 
— to exhaust the air in a given receiver, and to furnish 
a steady stream of 
air, just as the force 
pump does of wa- 
ter. The term air 
pump is usually re- 
served for instru- 
ments of the first 
class, while air com- 
pressor and blow- 
ing engine are used 
for the latter. In 
the ordinary air 
pump (Figs. 80 and 
81) the valves are 
just the same as 
those in the water 
pump. The receiver to be pumped out is commonly a glass 

bell jar resting on a carefully 
ground brass plate, from the 
center of which a tube passes 
to the cylinder of the pump. 
The valve (b) at the end of 
this tube opens into the cylin- 
der. A second valve ($), often 
for convenience located in the 

U piston itself, opens from the 

cylinder into the atmosphere. 
At every up-stroke the air in 
Fig. 8i.-Air pump. the receiver expands into the 

cylinder ; at every down-stroke 
b closes, and the air in the cylinder passes through a into 
the outer atmosphere. It is impossible in this way to get a 




Fig. 80.— Air pump. 




PRINCIPLES OF FLUID PRESSURE 



131 



«U^Q 



perfect vacuum in the receiver, for finally the residual air 
has not tension enough to open the valve b. It is also 
impossible, theoretically, since any process which removes a 
fractional part of air then in the receiver must always leave 
a residue of air. A small pressure gauge constructed on 
the same principle as the manometer shows exactly the 
amount of residual pressure — usually only a few millimetres 
of mercury. For most purposes the air pump is perfect 
enough, and allows many interesting experi- 
ments — such as removing the air from the 
Magdeburg hemispheres, from the apparatus 
known as the " Fountain in Vacuo," etc. 

145. The Mercury Air Pump (Fig. 82).— 
This is constructed on the principle of the 
barometer, and what we get is really a Torri- 
cellian vacuum. As the pellets of mercury 
fall down the tube they form little air-tight 
pistons ; but gravity being a constantly accel- 
erating force tends to make these pellets go 
faster and faster. Consequently, they get 
separated by small vacuous spaces, and as 
these pass the opening a into the receiver, 
the air in the receiver expands and fills these 
spaces. In this way the air in the receiver 
becomes more and more rarefied, and as there 
are no valves to be opened the exhaustion can 
be carried to a high degree of perfection. 
The residual pressure is shown at any time 
by subtracting the height of the column of mercury, 1) c, 
from the barometric height. If these columns were equal 
it would indicate a perfect vacuum. 

146. The Water Exhaust (Fig. 83).— In the laboratory it 
often happens that we want an exhaust at hand without our- 
selves doing the pumping. Running water permits such an 
exhaust with the least inconvenience. The principle is simi- 
lar to that of the mercury pump, but we give the water as 



1 



Fig. 82.— Mer- 
cury pump. 



132 



PHYSICS 



great velocity as possible by making it escape through a 
tapering nozzle. In this way the water carries part of the 
air away with it, and produces a partial vacuum. 

147. Air Compressors and Blowing Engines.— By reversing 
the valves in the usual type of air pump, we have a pump for 
compressing air (Fig. 84). Each down-stroke of the piston 
closes the valve «, compresses the air in the 
cylinder, opens the valve #, and forces the air 
into the compressed-air receiver. It is manifest 
that this simple instrument may serve at least 
three purposes : 1. It may be used to exhaust 
the receiver A. 2. It ___________ 

may be used to condense 
gas in the 
3. It 



Water 




may 



receiver B. 
be used for 



Air 



I 



Fig. 83.— Wa- 
ter exhaust. 



transferring gas from one receiver to another. 

There are many modifications of the pump 
and many practical applications, such as the 
bicycle pump, pump for the compressed-air 
brake in use on all modern trains, for the com- 
pressed illuminating gas used in many railway 
cars, for testing the gas pipes in our houses, for 
producing sprays in medical treatment, and so 
on. The most important application is in the 
powerful blowing engines used at all blast fur- 
naces. 

148. Siphons. — The siphon is a very simple device for 
transferring fluids from one level to a lower level over an in- 
tervening obstacle. Siphons depend for their action upon 
two principles — the pressure of the atmosphere and the 
tendency of all fluids to seek their own level. They will 
not work in a vacuum, and they will not raise fluids to a 
height greater than that of a barometer filled with the 
fluid in question — that is, 76 centimetres in the case of 
mercury, or 1,033 centimetres in the case of water. 

Let us analyze the simplest form of siphon, a U-shaped 



PRINCIPLES OF FLUID PRESSURE 



133 





tube of glass with one leg longer than the 

other. Suppose it to be in operation, trans- 
ferring water from the level bto the level c 

over the intervening obstacle, represented 

by the wall of the vessel (Fig. 85). The 

atmosphere acts on the surface of water in 

both vessels with an equal pressure, which 

we may represent as li. There is also at 

the level c in the lower vessel a downward 

pressure of a column of water of height a c, 

and further, at the level 5, in the upper 

vessel, a downward pressure 

of a column of water, a b. 

The downward pressure in 

the longer leg of the siphon 

therefore exceeds the down- 
ward pressure in the shorter leg by the 

weight of a column of water, b c. Water 

consequently flows over the arch of the 

siphon and into the lower vessel, and con- 
tinues to flow either until the upper vessel 

is emptied or the level of water is the same 
in both vessels. Ap- 
parently the atmos- 
phere has nothing to 
do with it, but imagine 
for a moment the absence of atmos- 
phere. The only force being gravity, 
the water would flow down in both legs 
of the siphon, and we should simply 
have a vacuum in the tube. Or, imag- 
ine an atmosphere, and make a b 40 
feet. Suppose the siphon completely 
filled with water and free to act. At 

once the water would separate in the arch of the siphon 

and sink to a height of about 34 feet in each of the legs. 





Fig. 84.— Com- 
pressor. 



Fig. 85.— Siphon. 



134 



PHYSICS 



There would be a barometric vacuum in the arch and no 
flow of water whatever. 

A piece of rubber hose completely filled with water and 
dipping under the surface of water in two vessels at dif- 
ferent levels often serves as a convenient siphon, and is 
somewhat easier to fill and start than a rigid glass tube. 

Aspirating Siphon (Fig. 86).— The difficulty of filling 
and starting the plain glass siphon is so considerable, and 
especially in the case of sulphuric acid and other chem- 
icals not to be freely handled, that a modification of the 

instrument has been de- 
vised known as the aspi- 
rating siphon. In this a 
second tube leads upward 
from near the bottom of 
the longer leg, and after 
swelling into a little bulb 
near the top is turned at 
right angles and formed 
into a mouthpiece. To 
start the siphon the short- 
er leg is dipped into the 
liquid in the upper ves- 
sel and the longer leg 
is closed either by the 
thumb, if the liquid be 
harmless, or by a stop- 
cock if harmful. The 
mouth is then applied to 
the mouthpiece and the 
air sucked out of the two 
tubes. The liquid rushes over and fills both tubes. The 
bulb is intended to show the operator more plainly when 
the liquid is getting dangerously near his mouth. . The 
suction is stopped and the longer leg of the siphon is 
opened. The liquid flows over as in the plain siphon, and 




Fig. 86. — Aspirating siphon. 



PRINCIPLES OF FLUID PRESSURE 



135 



the aspirator has no further influence. Great care must 
be taken not to get acid or other dangerous chemicals into 
the mouth. 

Fountain Siphon (Fig. 87). — The siphon may be given 
a multitude of forms, and may be very ingeniously modi- 
fied. A very pretty form is the 
fountain siphon. A round-bottom 
Florence flask is fitted with a doubly 
perforated rubber stopper, and is 
supported in an inverted position. 
A straight glass tube passes through 
one of the perforations (preferably 
in the middle of the stopper) and 
ends inside the flask in a fine jet. 
A second tube passes through the 
other perforation, and with the ad- 
dition of a rubber hose forms the 
long leg of the siphon. It is easy 
to start the fountain by having a 
little water in the flask before it is 
stoppered. When the flask is in- 
verted the water runs out the open 
tube into the hose, and at once the 
fountain begins to play. If the difference of level in the 
two vessels is considerable the water rises in a single thread 
and strikes against the walls of the flask with no little 
force. 

149. Siphoning Gases. — It is quite as possible to siphon 
gases as liquids. If the gases are heavier than air we do it 
right side up ; if lighter than air we do it upside down. Let 
us take two large battery jars (Fig. 88) and fill the upper one 
with carbon-dioxide gas (C0 2 ), sp. gr. = 1.56. This gas can 
easily be made by placing fragments of marble (CaC0 3 ) in a 
gas-generating flask with a little water, and adding hydro- 
chloric acid (HC1) through the thistle tube. C0 2 is given 
off copiously, and by means of a rubber hose may be con- 




Fig. 87.— Fountain siphon. 



136 



PHYSICS 




Fig. 88. 



ducted into the upper jar. The C0 2 is quite 

invisible, but it extinguishes a flame at once, 

and so a burning match will tell us 

when the jar is full. A lighted candle 

is placed in the lower jar. By 

means of the aspirating siphon, 

or a bit of rubber tubing, 

a stream of C0 2 is now 

made to pass over 

the upper jar. The 

gas stream is, of 

course, invisible, 

but it will be no- 
ticed that the can- 
dle burns less and 

less brightly, and 

finally flickers and 

goes quite out. 

In the case of light gases like hydrogen (H), sp. gr. = 

.069, both the gas jars and the siphon are inverted, and the 
H passes 'from the lower to the higher jar. 
At the beginning of the experiment the lower 
jar is filled with H, the upper jar with air. 
At the end the H is in the 
upper jar. It, too, is invisi- 
ble, but its presence can be 
shown by applying the open 
end of the jar to a flame. 
A considerable explosion 
announces a mixture of H 
and air. 

150. Hero's Fountain 
(Fig. 90).— This bit of clas- 
sical apparatus, invented by 
Hero of Alexandria, 120 
B. c, deserves notice as an 




PRINCIPLES OF FLUID PRESSURE 



137 




^ 



interesting case of transmitted pressures. In starting the 
experiment M should be nearly full and N nearly empty 
of water. There must also be some water in the pool D. 
The column of water from the pool to the lower globe 
exerts a pressure upon the air in that globe which is trans- 
mitted through the tube to the air in the ^. 
upper globe and forces the water out in a 
jet. It is sometimes used for cologne foun- 
tains, and the liquid can be 
used over and over again by 
pouring it back from M to 
N each time it runs down. 
A cheaper form is shown in 
Fig. 91. It can be made 
out of three bottles and a 
little tubing. 

151. Tension inside the 
Barometer Tube. — If the 
space in the upper end of 
the barometer is a vacuum 
there is no tension there, 
and it is manifest that the 
walls of the tube must sus- 
tain in that part the whole 
atmospheric pressure of fif- 
teen pounds per square 
inch. If this portion of the 
tube were made of rubber, 
its sides would collapse un- 
der the pressure. How is 
it with other portions of the 
tube ? In the lower end of the tube, at the level of the mer- 
cury in the cistern, the outward pressure of the column of 
thirty inches of mercury must be equal to the inward pres- 
sure of the atmosphere. Here the tube might be made of 
the thinnest rubber and neither expand outward nor con- 



FlG. 90.— Hero's 

fountain. 



Fig. 91. 



138 



PHYSICS 




tract inward. Halfway up the tube the pressure from with- 
out is still that of an atmosphere, while the pressure from 
within is that of half an atmosphere— fif- 
teen inches of mercury. So it appears 
that while the pressure from without is 
fifteen pounds per square inch throughout 
the whole length of the tube, the pres- 
sure from within varies all the way from 
fifteen pounds at the lower end to zero 
at the upper end. A water barometer 
may be made of rubber tubing with a 
closed glass tube in the upper end, but it needs to be the 
thick-walled Bunsen pressure tubing. to prevent its sides 
from collapsing. If a pin-prick is made anywhere along 
the side of this tube, water does not leak out, but air leaks 
in. ,A water barometer must not be expected 
to stand thirteen and six tenths as high as the 
mercury barometer, although from considera- 
tion of specific gravity alone we might expect 
that. The tension of water vapor in the upper 
end of the tube depresses the column somewhat. 
152. The Inverted Tumbler of Water.— From 
the above discussion of tension inside the ba- 
rometer tube we naturally find an explanation 
for the time-honored experiment of the inverted 
tumbler of water (Fig. 92). The upward pres- 
sure of the air upon the paper which covers the 
mouth of the tumbler is fifteen pounds per 
square inch, while the downward pressure is 
merely the weight of the water so long as no 
air gets in to produce an internal tension. The 
experiment may even be performed by putting 
mosquito netting over a wide-mouth bottle full FlG 93 
of water, and it need not be tied or held in 
place ; atmospheric pressure will do that. Medicine drop- 
pers, students' lamps, fountain ink wells, fountain sponge 



PRINCIPLES OP FLUID PRESSURE 



139 



J-\ 



H 



cups, etc., all hold their liquids because atmospheric pres- 
sure from without is greater than the tension from within. 

153. The Specific Gravity of Liquids measured by bal- 
ancing them against Atmospheric Pressure. — Fig. 93 illus- 
trates a simple way of finding the specific gravity of liquids. 
One tube dips into a vial of water and the other into a vial 
of liquid whose specific gravity is to be found. When a 
person applies his mouth to the tube e and reduces a little 
the tension of the air in the tubes, the atmospheric pressure 
forces each liquid up its respective tube, and by comparing 
the length of the columns it is possible to obtain the rela- 
tive weights. It is manifest that the col- 
umn of liquid c d must have the same 
weight as the column of water a #, since 
the weight of each column of liquid must 
be equal to the pressure of the air from 
without minus the tension .^ 
within. From this we r K 
should find that a column 
of water eight inches long 
balances a column of alco- 
hol about ten inches long. 

154. Fluids in Motion. — 
It is to be noted that in 
all our stud3 r of fluids thus 
far we have considered 
them in a state of rest, and 
thus the elements of fric- 
tion and momentum have not complicated our problems. 
In the apparatus illustrated in Fig. 94 the water in the tube 
stands at the same level as the water in the reservoir, but 
Fig. 95 illustrates the fact that the water will not flow in 
a fountain to the same level. Friction in the tube, the 
resistance of the air, and the interference of the falling 
drops of water, all act to prevent this. If the water in a 
system of city water works were absolutely at rest it would 



Fig. 94. 



Fig. 95. 



140 



PHYSICS 




rise in a house pipe as high as the level of the water in the 
reservoir ; hut the fact that the water is flowing continually 
through the pipes to supply so many faucets during the 
daytime prevents its rising to the upper stories of many of 
the houses in large cities, although the reservoir may be 
far above them. At night when less water is used it may 
rise even to tanks upon the roofs of these same houses. 

Water wheels and windmills are run by the momentum 
of the moving fluids rather than the pressure of those fluids 
at rest. The word hydrostatic refers 
to fluids at rest ; hydraulic refers to 
fluids in motion. 

155. The Hydraulic Ram. — This 
instrument depends upon the momen- 
tum of running water. The principle 
of it may be illustrated by a very sim- 
ple piece of apparatus. 

Let the two reservoirs A and B 
(Fig. 96) be connected by a rubber 
tube. The end of the tube in A is 
supplied with a valve which prevents 
the fluid returning from A. If we 
seize the rubber tube at b and raise it 
a few inches and then let it fall with 
a sudden jerk, the momentum of the 
moving column of water will push a 
small amount of water up through 
the valve in A. By repeating this 
movement several times B may be 
emptied of its water and carried above 
its level in A. This is the idea which 
underlies the hydraulic ram, whereby water is made to. flow 
from a source upon a hillside, first down into a valley, and 
then to a house farther up the hillside than the source. 
In order to accomplish this a portion of the water must 
run to waste. It is the energy of this portion of the water 



Fig. 96.— Principle of 
hydraulic ram. 



PRINCIPLES OF FLUID PRESSURE 



141 



that does the work of lifting the other portions of the 
water to the house. A diagram will make the mechanism 
plain. 

D (Fig. 97) is the spring from which water is to be car- 
ried through a pipe C to a house which is higher than the 
spring. If the valve A should remain closed, water would 




Fig. 97. — Diagram of hydraulic ram. 



stand at the same level in C as at D ; but the valve A is 
made heavy enough to sink in quiet water. As soon as it 
sinks, however, the water ceases to be quiet, and rushes out 
through the orifice above with such a rush as to toss the 
valve shut again with a smart thump. When the flow of 
the water is thus suddenly stopped at A its momentum 
forces open the valve b, and some of it passes in to com- 
press the air in the chamber B. At the rebound of this air 
the valve b closes and some water is forced higher up the 
tube C leading to the house. As soon as the water in the 
apparatus becomes quiet the valve A sinks again, and the 
events just described are repeated. 



HEAT 

CHAPTER, XVIII.— How Heat is produced 

156. General Definition of Heat. 

157. Heat produced by Friction. 

158. Heat produced by Percussion. 

159. Heat produced by Pressure. Figs. 98, 99, and 100. 

160. Heat produced by Chemical Action. 

161. Other Sources of Heat. 

CHAPTER XIX.— Some Effects of Heat 

162. General Statement. 

163. Expansion of Solids. Fig. 101. 

164. Applications. 

165. Irregularities. 

166. Expansion of Liquids. 

167. Measurement of Temperature by the Expansion of Mercury in the 

Thermometer. Figs. 102 and 103. 

168. Centigrade, Reaumur, and Fahrenheit Scales. Fig. 104. 

169. Conversion of one Scale into another. 

170. Self-recording Thermometers. Fig. 105. 

171. Expansion of Gases. Correction of Volume for Temperature. 

172. The Air Thermometer. Fig. 106. 

173. Pyrometers. 

174. Range of Temperatures. 

175. Relation of Temperature to Animal and Vegetable Life. 

176. Heat determines the State of a Substance. 

177. Fusion. 

178. Change of Volume due to Fusion. 

179. Change of Fusing Point under Pressure. 

180. Effect of Alloys upon Fusing Point. 

181. Vaporization. 

182. Five Factors of Evaporation. 

183. The Evaporation of Solids. 

184. Vapors. 

185. Critical Temperature. 

186. Boiling. Fig. 107. 

187. Laws of Boiling and Table of Boiling Points. 

188. Changes in the Boiling Point. 

189. Determination of Altitude by Thermometers. 

190. Saturation. 

143 



144 PHYSICS 

191. Vapor in the Air. — Dew Point. 

192. Humidity. Fig. 108. 

193. Rainfall. 

194. Moisture and Health. 

195. Illustrations. 

196. Condensation, Solidification, and Crystallization. 

CHAPTER XX.— How Heat is transferred 

197. General Statement. 

198. Conduction. Fig. 109. 

199. Applications. 

200. Convection. Figs. 110 and 111. 

201. Radiation. 

202. Absorption, Radiation, and Reflection. 

203. Relation of Heat and Light. 

204. Radiometer. Fig. 112. 

CHAPTER XXI. — Calorimetry and Specific Heat 

205. Measurement of Heat. 

206. Temperature. 

207. Quantity of Heat. 

208. Specific Heat. 

209. Determination of Specific Heat. 

210. Applications. 

CHAPTER XXII.— Latent Heat 
A. Heat disappears when Solids liquefy 

211. Heat Latent in Solutions. 

212. Freezing Mixtures. 

B. Heat disappears when Liquids vaporize 

213. Heat Latent in Vapors. 

214. Absolute Temperature. 

215. The Production of Cold. 

216. Expansion of Gases. 

217. Cold by Evaporation. Fig. 113. 

C. Heat reappears ivhen Vapors liquefy 

218. Heat recovered from Vapors. 

D. Heat reappears when Liquids solidify 

219. Heat recovered from Solutions. 

220. Recapitulation. 



CHAPTEE XVIII 

HOW HEAT IS PRODUCED 

156. General Definition of Heat. — In studying heat, we 
study only a particular form of energy — molecular motion 
— and all that we have learned about motion in general is 
applicable to the motion of molecules. Like all forms of 
energy, heat represents two elements — matter and motion. 
It is a measurable quantity, and the measurement may be 
made with respect to the two aspects of energy studied in 
mechanics— that is, to the degree or intensity of motion 
and to the total amount of motion or momentum. By the 
degree or rate of motion we mean speed or velocity, meas- 
ured in centimetres per second. This measurement is inde- 
pendent of the amount of matter. In the case of heat we 
can not measure the velocity directly in centimetres. The 
motion, being molecular, is quite invisible. It consists of a 
to-and-fro motion, a vibration, and not of a plain and sim- 
ple change of position. We can only measure the intensity 
of the molecular motion by means of its effects, and this 
we do with a thermometer (section 167). 

The total amount of motion, or momentum, is the prod- 
uct of mass and velocity, or m v. 

In heat the amount is measured in the same way. It is 
the degree of heat motion multiplied by the mass of the 
matter in motion. But here, again, the measurement must 
be conventional, since the degree of heat motion can not 
be measured in absolute units. The measurement of heat 
11 145 



146 PHYSICS 

quantities is treated under the head of Calorimetry (Chap- 
ter XXI). 

The term heat is used in two very different senses. 
First, the physical sense, the molecular motion of a body ; 
and, second, the physiological sense, the sensation produced 
in us by contact with a hot body. We shall use it always 
in the physical sense, to represent the thermal condition of 
a body. We can not judge of this accurately by means of 
our own sensations, for hot and cold are merely relative 
terms. When we come in from the cold a moderately warm 
room seems hot to us, and when we pass from an overheated 
room into a moderately warm one it feels cold to us. 

Neither can we judge of the relative heat of two bodies 
by simply touching them, for the sensation produced does 
not depend alone upon the degree of heat in the bodies 
touched, but also upon the relative speed with which they 
give up or absorb heat when brought in contact with the 
hand. Thus, pieces of iron and of wood may be equally 
hot, but to the hand the iron will seem much the hotter, 
because it gives up its heat more readily than the wood. 
The two may be equally cold, but not to the touch ; the 
iron will seem much the colder, because it takes away heat 
more rapidly from the hand. On a cold morning we instinc- 
tively avoid handling all metal objects, but we pick up wood 
or cloth without hesitation, although they are all of the 
same, or nearly the same, temperature. 

Until the end of the eighteenth century it had been 
believed by many eminent philosophers, among whom was 
Sir Isaac Newton, that heat was a very subtle fluid that 
more or less completely filled the pores of all substances, 
and could be transferred from one to another, much as 
water flows from one vessel to a communicating one, and 
only comes to rest when the level is the same in both. In 
the closing years of that century two celebrated experi- 
ments were made, that showed once for all that heat is not 
a substance, but is simply a motion of the molecules. 



HOW HEAT IS PRODUCED 147 

An American, Benjamin Thompson, afterward Count 
Eumford, had charge of the boring of cannon in the arse- 
nal at Munich, and, observing that great heat was produced, 
he became interested to investigate the matter. He found 
that by immersing the cannon in water and by purposely 
using a very blunt boring tool he could easily produce 
enough heat to make the water boil. He rightly reasoned 
that what could be produced in such unlimited quantity by 
the expenditure of mechanical energy must itself be a form 
of energy. He even established a rough relation between 
the amount of mechanical energy that disappeared and the 
amount of heat that took its place. This was in 1798. The 
year following, Sir Humphry Davy showed that two pieces 
of ice rubbed together below the freezing point could be 
melted by the heat of friction. 

At the present time no one seriously doubts that heat is 
a mode of motion — that is, a form of energy ; but it took 
the first third or even the first half of the nineteenth cen- 
tury to establish the doctrine on firm scientific grounds. 
The final victory was gained by the experiments establish- 
ing the exact quantitative relation between heat and me- 
chanical energy — that is, the mechanical equivalent of heat 
— work that will always be associated with the name of the 
English scientist Joule. The doctrine has been theoretic- 
ally worked out by such men as Clausius, Helmholtz, Tait, 
and Maxwell, and made popular by Tyndall and other able 
experimenters. 

Heat, from the standpoint of physics, is a vibration of 
molecules— the greater the amplitude of vibration the more 
intense the heat. From the standpoint of physiology it is 
an irritation of certain nerve endings b;y appropriate means 
— as, for example, the pelting of these vibrating molecules 
of matter against the skin. 

Since heat is a form of energy — one variety of molecu- 
lar motion — it can only be produced by the transformation 
of some other form of energy into heat. This is accom- 



148 PHYSICS 

plished so readily that heat has been called the currency, 
or medium of exchange, in the realm of energy. We may 
therefore expect to find that there are a great variety of 
ways of producing heat. 

157. Heat produced by Friction. — When mechanical mo- 
tion is interrupted in any way, as in friction, we have the 
movement of the whole transformed into a movement of 
the parts — that is, into heat. We do this when we rub our 
hands together on a cold morning. A coin or other bit of 
metal rubbed against a flannel blanket or against our coat 
sleeve becomes uncomfortably warm. It is quite possible to 
measure the relation between mechanical motion and heat 
— the quantity of heat that corresponds to a given amount 
of mechanical energy. In this way we may get the thermal 
equivalent of motion, or the mechanical equivalent of heat. 

It is a familiar fact that machinery warms up while 
running. It has already been said that the work done by 
any machine is never fully equivalent to the power applied 
to it. The loss is due to friction, and the heat which warms 
up the machine while in motion is the equivalent of this 
apparently lost energy. Anything which will reduce fric- 
tion should therefore diminish this loss. Hence we oil the 
machine when we desire it to perform work rather than 
produce heat. 

The relation between heat and work constitutes a dis- 
tinct branch of physical science called thermodynamics. It 
expresses the quantitative relation between two important 
forms of , energy, and is an application of the doctrine of 
the conservation of energy. 

158. Heat produced by Percussion.— When a bullet strikes 
a target its mass motion is converted into molecular motion, 
or heat. When we hammer a nail, both the hammer and 
the nail become hot ; the pile driver and the pile become 
hot in the same manner. The earth is moving through 
space, around the sun, at the rate of about nineteen miles 
per second. Could it be stopped, its motion would be 



HOW HEAT IS PRODUCED 



149 



transformed into heat, and this would be sufficient to 
vaporize the entire earth. Indeed, that is precisely what 
is happening to hundreds of meteors which daily fall into 
the earth's atmosphere. In 1854 Sir William Thomson 
concluded that the heat of the sun was chiefly due to the 
percussion of meteors which fall upon it. 

159. Heat produced by Pressure. — When gases are con- 
densed by a pump, temperature rises (Fig. 98). When they 
are allowed to expand again they return 
to their original temperature. If, while a 
gas is under pressure, the heat is conducted 
off and the pressure is then removed, the 
expansion will cause the temperature to 
fall as far below the original temperature 

as it was raised above 

that by pressure. This is 

well illustrated in cer- 
tain ice machines, where 

the heat produced, by 

pressure is removed by 

running water, and the 

cold which is produced 

by the sudden expansion 

of the gases is sufficient 

to freeze water. (See 

also 216.) 

It is pretty generally 

known that water boils at 

212° Fahrenheit. With- 
out extra pressure its temperature can not be raised above 
that point. We may, however, raise it to any desired tem- 
perature by putting its steam under sufficiently great pres- 
sure (Fig. 99). Because of great -pressure, steam in a loco- 
motive boiler is much hotter than 212°. When this steam 
issues in a jet, however, the sudden expansion reduces its 
temperature, so that it is only lukewarm (Fig. 100). 





Fig 



Fig. 98.— Heat by 
pressure. 



-Tempera- 
ture of steam un- 
der pressure. 



150 



PHYSICS 




The internal heat of the earth may be due to the pres- 
sure of its mass. The rise in temperature is about one 
degree Fahrenheit for every fifty or sixty feet of descent 
varying much in different localities. It must be understood' 
that motion must result from pres- 
sure in order to produce heat— that 
is, the earth must be still contracting 
under its own weight if heat is being 
now produced. But the internal heat 
which was produced in former cen- 
turies by this contraction has very 
great difficulty in getting away from 
the, earth. It has been estimated that 
so little of it reaches the surface as 
to effect a rise in temperature of only 
FlG 100 one thirty-sixth of a degree. So like- 

wise the heat of the sun may be pro- 
duced chiefly by the action of gravitation in pulling its par- 
ticles of matter nearer together. Von Helmholtz calcu- 
lated that all the sun's heat for a year would be produced 
by the contraction of thirty-eight metres in its radius. If 
it continues to give out heat at the present rate for four 
million years, it will then be contracted to half its present 
diameter. 

The total heat sent to the earth annually from the sun 
would be capable of melting a sheet of ice fifty-four metres 
thick, extending over the whole surface of the globe. The 
earth, being distant about ninety-two million miles from the 
sun, receives only the one-twenty-one-hundred-millionth part 
of the entire amount of heat which the sun sends forth on- 
all sides. How the sun's heat is transmitted through space 
from the sun to the earth, and what transformations it 
passes through after it reaches the earth, will be discussed 
in other chapters. 

160. Heat produced by Chemical Action.^The process 
of ordinary burning, or combustion, is the union of a sub- 



HOW HEAT IS PRODUCED 151 

stance with oxygen. Burning, combustion, and oxidation are 
nearly synonymous terms. The process, however rapid, as 
in the case of combustion, or slow, as in the case of the rust- 
ing of a metal, is always accompanied by the production of 
a definite amount of heat, which bears a fixed ratio to the 
amount of chemical action. 

The familiar instance of the slaking of lime with water 
is an illustration of the production of heat by chemical 
action. Both the lime and the water may be very cold, but 
when they are mixed their atoms clash together in forming 
a new compound, and the molecules of the new substance 
are left in a state of vibration so intense as to cause the 
water to boil, or even to set wood on fire. Storehouses of 
lime frequently take fire by rain leaking in upon the lime. 
Ships loaded with lime are in similar danger. Compost 
heaps get very warm by reason of the slow chemical decom- 
position that is going on in them. Piles of green grass, 
new grain, new hay, new flour, cotton with seed in it, or 
oily cotton waste, all produce heat for the same reason. 
Animal heat is produced in like manner. Most of our 
foods are particularly liable to chemical change ; indeed, 
their value as foods depends upon this characteristic. Ani- 
mal heat is due chiefly to the breaking down of these com- 
pounds in the body. 

161. Other Sources of Heat. — Electricity is one of the 
latest sources of heat to be utilized by man. We shall see, 
when we come to this subject, that whenever a current of 
electricity meets resistance in its passage, heat is produced. 
This is sufficient to cook with in the electric stove. Our 
electric cars are warmed in winter by turning electric 
energy into heat. Heat is produced from the electric cur- 
rent for welding metals and for fusing the most refrac- 
tory substances. AYe shall study this matter more in detail 
under Electricity. 



CHAPTEK XIX 

SOME EFFECTS OF HEAT 

162. General Statement. — A body at a given tempera- 
ture possesses a definite kinetic or molecular energy, and 
therefore displays definite qualities. If the temperature is 
that ordinarily experienced, and remains fairly constant, we 
are not apt to think of the qualities as the effect of heat. 
In looking at a sheet of water or at a bowl of mercury we 
are not apt to think of the liquid state of either as an effect 
of heat. We are more apt to consider it as an essential 
quality of the water or the mercury. But a scientific con- 
ception of the world about us requires that we shall regard 
everything not as fixed and permanent in itself, but simply 
as the effects of given conditions, and therefore only per- 
manent so long as these conditions are permanent. Changes 
of temperature, pressure, light, and electrical conditions 
produce corresponding changes in the qualities of things, 
and, if these changes are sufficiently great, produce a very 
different world. 

Solids, liquids, and gases are not such by necessity, but 
only so under the particular conditions which happen now 
to prevail. We can imagine a cold so intense that all things 
would be solid, and a heat so intense that all things would 
be gaseous. For example, many things which are in the 
liquid or gaseous state upon the earth, perhaps exist on 
the moon in a solid state ; and many things which are in 
the solid state on the earth exist on the sun in a gaseous 
state. 

152 



SOME EFFECTS OF HEAT 153 

The direct effects of heat become very evident when we 
keep all the other conditions constant and change only the 
heat conditions. We can do this by giving heat or by taking 
away heat. The most important effects are change of vol- 
ume and change of state. It is a common piece of every- 
day knowledge that heat expands and cold contracts. This 
may be observed on all sides ; and these observed facts help 
to establish our theory of the nature of heat. If heat be 
molecular motion, an increase of heat must mean an increase 
of molecular motion, and this very naturally would cause 
expansion, since the greater motion would require the 
greater space. In the same way a diminution of motion 
would mean contraction, since smaller space would natu- 
rally suffice for the smaller motion. Water is in the solid, 
liquid, or gaseous state, according to the amount of heat or 
molecular motion which it has. So it is with other sub- 
stances. 

163. Expansion of Solids. — Fig. 101 represents a ball 
which, when cold, will pass through the ring, but when it 

efficient of expan- FlG 101 _ Expansion by heat 

sion. This may 

be of the volume or of the length. The coefficient of vol- 
ume expansion is the increase of volume due to a rise of 
1° in temperature ; but for solids the coefficient of linear 
expansion is of greater importance practically. It is the 
increase of length due to a rise of 1° in temperature. It 



154 PHYSICS 

is determined by taking a bar of the material of unit cross- 
section, one square centimetre, making two marks on the 
bar, one near each end, measuring the distance between 
them very accurately, and noting the temperature. The 
bar is then brought to a higher temperature by surround- 
ing it with steam. The distance between the two marks 
is now measured. From this is calculated the increase of 
length for 1° rise in temperature. For example, wrought 
iron is found to expand by a twelve-millionth part of its 
length for 1° rise in temperature. That is, a wire of this 
material one mile in length, or 63,360 inches, would expand 
TooVo oo °f 63,360 inches, or about three quarters of an inch 
for 1° rise in temperature; for 10° it would expand 7.5 
inches, and for 100° it would expand about 75 inches, or 
6 feet. 

TABLE OF LIKEAB COEFFICIENTS. 



Flint glass 000008 

Platinum 000009 

Wrought iron 000012 

Gold 000015 

Copper 000017 



Brass 000019 

Silver 000019 

Tin 000022 

Zinc 000029 

Lead 000028 



164. Applications. — Iron tires are clasped around wheels 
while still quite hot, so that their contraction may press 
the rims more firmly on the spokes, and the spokes more 
firmly into the hub. For the same reason sheet-iron plates 
are fastened together, as in boilers, by red-hot rivets. When 
the rivets cool they contract, and bind the plates together 
with tremendous force. Bulging walls are sometimes brought 
to place by passing hot iron rods through them. The con- 
traction of the rods brings the wall back into place. Dial 
thermometers operate through the expansion and contrac- 
tion of metal spirals whose motion is communicated by a 
system of levers to the pointer over the dial. 

But not only do we utilize the tremendous force of con- 
traction and expansion, but we are also obliged in many 



SOME EFFECTS OF HEAT 155 

instances to provide against it in order to avoid disaster. 
Thus, the ends of steel rails must have a little free space 
between them, or in hot weather they would force each 
other out of line. In the same way, sections of an iron 
bridge must have sufficient play to prevent harmful tension 
or pressure. Some of our most appalling railroad accidents 
have been caused by the contraction and consequent break- 
ing of iron rods. The Brooklyn Bridge is not far from a 
yard longer in summer than in winter, owing to the expan- 
sion of the suspending cables. 

Glass lamp chimneys, tumblers, bottles, etc., crack when 
heated in one part only, because of the stress produced by a 
greater expansion in one part than another. Such things 
may be heated safely if put in an oven or immersed in 
water and heated gradually, so that all parts may expand 
alike. Thin glassware, used for test tubes, beakers, flasks, 
and the like in the chemical laboratory, may safely be 
heated in one part more than another because of its flexi- 
bility. The most common cause of disaster to this glass- 
ware in the laboratory is a drop of liquid coming in contact 
with dry, hot glass. The contraction due to sudden cooling 
in one spot shatters the glass. We may heat it wet or heat 
it dry, but we may not wet it while hot. 

The expansion and contraction due to changes in tem- 
perature causes cracks to start in the more brittle rocks, 
such as the trap rocks of the Palisades and other highlands. 
Water gets into these small cracks, and in winter freezes. 
This, as we shall learn in section 178, causes expansion. 
Thus, the summer's sun and the winter's frost conspire to 
tear down the mountains. 

Ice expands and contracts with changes of temperature. 
This may account for the snapping and cracking of the ice 
on a still pond in very cold weather. 

165. Irregularities. — In general, solids expand equally 
in all directions, but there are certain crystals that are an 
exception to this rule. On being heated, they expand most 



156 PHYSICS 

along one principal axis, and may even contract at right 
angles to this direction. This is the case with Iceland spar. 

There are variations in the coefficients of expansion at 
different positions on the thermometer scale, the coefficient 
increasing slowly with the temperature. The values given 
in the table are, however, sufficiently accurate for all prac- 
tical uses. 

166. Expansion of Liquids. — Since liquids have no defi- 
nite shape, but assume the form, of the containing vessel, 
we can only measure the increase of temperature — that is, 
their coefficient of volume expansion. Since the contain- 
ing vessel also changes its volume with change of tempera- 
ture, all determinations of the expansion of liquids must 
take this into account. In general, the change of volume 
is very small. The coefficient rises with the temperature. 
Water and mercury are the two liquids whose coefficients 
of volume expansion are of the largest importance. Water 
presents the curious case of a liquid which does not expand 
uniformly with the application of heat. A body of water 
at the freezing point — 32° on our ordinary thermometers — 
on being heated, contracts in volume until it reaches 39°. 
It then begins to expand, and at 46° has the same volume 
as at 32°. Beyond this point the expansion proceeds con- 
tinuously until the boiling point, 212°, is reached, and the 
watei passes into steam. Thirty-nine degrees is therefore 
known as the point of maximum density of water. 

This irregularity in the behavior of water has the utmost 
significance in the economy of Nature. Bodies of water, 
such as ponds and lakes, cool at the surface. The upper 
layers in growing cold also grow heavy, and sink to the 
bottom. This process continues until the whole body of 
water has a temperature of 39°. When this point is reached 
a further loss of heat makes the surface layers lighter as 
well as colder, and they consequently remain on top. When 
they reach 32° ice forms and shuts off the under water from 
any further large loss of heat. As both ice and water are 



SOME EFFECTS OF HEAT 



157 



poor conductors, the lower strata of water remain at 39°, 
and the water life is preserved. If water continued to grow 
heavier down to 32°, the ice would form at the bottom of 
all bodies of water, and the hottest of summer suns would 
hardly suffice to melt it. 

The ordinary thermometer is an illustration of the ex- 
pansion of liquids by heat. Mercury and alcohol expand 
by heat with sufficient regularity so that we use them to 
measure rise and fall in temperature. 

167. Measurement of Temperature by the Expansion of 
Mercury in the Thermometer. — All ordinary temperatures 
are measured by means of a well-known instrument — the 
thermometer. This depends for its 
action upon the effect 
of heat in making 
fluids expand. Alco- 
hol was formerly used, 
and for low tempera- 
tures is still used, but 
mercury has been sub- 
stituted for the al- 
cohol in nearly all 
instruments for every- 
day use. As the tem- 
perature rises, mer- 
cury expands, but the 
increase of volume is 
so slight that, unless 
-r-srl ^HF we em ploy some spe- 
" • 1 **" cial device for render- 

ing the expansion vis- 
ible, we should hardly 
be the wiser. This special device is very simple. We have 
a glass bulb capable of holding an appreciable amount of 
mercury, and provided with a fine capillary tube as its only 
outlet. In this way we have a considerable body of mer- 





Fig. 102. 



Fig. 103. 



158 



PHYSICS 



cury to expand and contract, but any change in its volume, 
however slight, makes a very noticeable change in the length 
of the column of mercury in the capillary tube. Heat also 
expands the glass bulb, giving it greater capacity, so that 
the first effect of heating a thermometer is to make the 
column of mercury sink ; but as soon as the mercury also 
becomes heated, the column of mercury rises, and quite 
enough for our purpose, since the increased volume of mer- 
cury is greater than the increased capacity of the bulb. 
What we really measure is their difference. 
The coefficient of volume expansion for mer- 
cury is .0001817, and for glass .0000254. 
The difference between these coefficients, 
.0001563, represents the apparent expansion 
of mercury in glass. 

Pure water, under a pressure of 760 milli- 
metres of mercury, always freezes and boils 
at the same temperatures, and so we take 
these as fixed points of temperature. Figs. 
102 and 103 show how these points are found 
when the thermometer is made. 

168. Centigrade, R6aumur, and Fahrenheit 
Scales. — There are unfortunately three differ- 
ent scales of temperature used in civilized 
countries. * 

Centigrade Scale. — In this the freezing 
point of water is called 0°, and the boiling 
point 100°. The varying temperature of 
liquid water is thus expressed in one hundred 
steps, hence the name. This scale was sug- 
gested by Celsius, a Swedish scientist, and is 
used in all scientific work, because of all the 
scales it is the most rational and convenient. It is also in pop- 
ular use in France and in the Eomance countries generally. 
Reaumur Scale. — The freezing point of water in this 
scale is also called 0°, but the boiling point is marked 80°, 



2 * 
o 

Fig. 104. 



SOME EFFECTS OF HEAT 159 

and the degrees are therefore larger than in the centigrade 
scale. It was devised by Reaumur, of France, and has 
nothing to commend it. Curiously, it is in popular use in 
Germany and Switzerland. 

Fahrenheit Scale. — This is the least admirable of the 
three. The freezing point is marked 32°, and the boiling 
point 212°, thus making 180° between the two points. The 
zero of the scale is therefore 32° below freezing, and is the 
point that was erroneously supposed to mark the greatest 
artificial cold producible. This scale is unfortunately the 
one in common use in the United States, in Great Britain, 
and in all English-speaking countries. It was devised by 
Fahrenheit, a German philosopher. 

Not one of these scales is used in the country where it 
originated. 

169. Conversion of One Scale into Another. 

1. Fahrenheit into Centigrade. — To change any Fahren- 
heit reading into centigrade, we must first subtract 32°, in 
order that both readings may count from the same starting 
point, the freezing point of water. The remainder is then 
multiplied by f , since 180° F. = 100° 0. Putting this into 
a compact formula, we have 

0.=f(P.-32) (1) 

Illustrations : Suppose the Fahrenheit reading was 212° 
(boiling point in F.), then 0. = {- (212 - 32) = f (180) = 100° 
(boiling point in C). 

2. Centigrade into Fahrenheit. — In this case we multiply 
the C, reading by f, since 100° C. = 180° F., and then add 32, 
or F. = |C. + 32 (2) 
Suppose C. = 100°, then F. = f 100 + 3.2 = 180 + 32 = 212°. 
By making C. = F. in either (1) or (2) we can find the point 
where both scales have the same reading. Thus : 

F. =f F. + 32 
5 F. = 9 F. + 160° 
4 F. = - 160° 

F. = - 40° = C. 



160 PHYSICS 

3. Reaumur and Fahrenheit. — In the same way by using 
f and |, since 180° F. = 80° E., we may turn E. and F. about 

E. = i (F. - 32) (3) 

F. = |E. + 32 (4) 

4. Centigrade and Reaumur. — Since 100° C. = 80° E., we 
have C. = | E., and E. = £ 0. (5) 

In nearly all German towns there is a public bathing 
place, where university professors and college students and 
schoolboys go in warm weather for a daily swim. In some of 
the places the temperature of the water in degrees Eeaumur 
is posted up each day, so that one may decide for or against 
a plunge. In the same way the regulations in German art 
galleries state in terms of Eeaumur the allowable variation 
in temperature. 

170. Self-recording Thermometers. — It is sometimes desir- 
able to have an instrument which will record either its own 




Fig. 105. — Maximum and minimum thermometers. 

extremes or its whole variation. The maximum and mini- 
mum thermometer does the former, and Draper's the latter. 
In the first, two thermometer tubes are mounted horizon- 
tally on the same scale board. The maximum thermometer 
has a small indicator, usually a bit of glass, inside the tube, 
which the expanding mercury pushes in front of it, but 
fails to pull back when it retreats itself. In this way we 
have a record of the highest temperature reached. The 
minimum thermometer is filled with colored alcohol, and car- 



SOME EFFECTS OF HEAT 161 

ries a little rider inside the fluid, which is so arranged that 
it will retreat with the alcohol, but offers too much friction 
when going in the other direction to advance with the alco- 
hol. In this way we have a record of the lowest tempera- 
ture reached. Such instruments are often used in green- 
houses and other places where a narrow range of tempera- 
ture is necessary for success. 

In meteorological stations a more complete record is 
wanted. In Draper's self-recording thermometer a pointer, 
moved by the expansion and contraction of metallic bars, 
traces its own movements on cards prepared for the pur- 
pose and made to rotate back of the pointer by means of 
clockwork. Or the fluctuations of a column of mercury 
may directly photograph themselves on a roll of slowly 
moving sensitive paper passing back of them. 

171. Expansion of Gases — Correction of Volume for Tem- 
perature. — We have in gases the most perfect example of 
expansion and contraction. A cubic foot of any gas meas- 
ured in winter may expand in summer so as to occupy 170 
cubic inches more than a foot. We have already found, 
from a study of Boyle's law (124), that the measured 
volume of a gas must be corrected for pressure. It is evi- 
dent, from what we have learned of the effects of heat, that 
the measured volume of gas must also be corrected for tem- 
perature. It was a French physicist, Charles, who in 1787 
first pointed out the law for the relation of volume of a gas 
to changes of temperature. The volume coefficients for 
different gases vary slightly, but in general may be stated 
to be .003663, or -^\^ of their volume at zero centigrade. 
That is, gas which would measure a cubic foot at 0° 0. would 
measure at 27° C, the temperature of a rather warm summer 
day (what would it be on Fahrenheit scale ?), 1 cubic foot -f- 
27 X .003663 cubic feet, or 170 cubic inches more than a 
cubic foot. If the volume V is given of any gas at 0° C, 
and we are required to calculate what its volume would be 
at a given temperature t higher than zero, we multiply V 
12 



162 



PHYSICS 




by 1 + .003663 t. If we are required to calculate what its 
volume would be at a given temperature below zero we 
multiply V by 1 — .003663 t. If the volume is given at a 
temperature above zero, and we are required to calculate 
what it would be at zero, we divide V by 1 +.003663 t. If 
the volume is given at a temperature below zero, and we are 
required to calculate what it would be at zero, we divide 
Fby 1 — .003663 t. 

172. The Air Thermometer.— The coefficient of volume 
expansion for air was found by Gay-Lussac by means of a 
thermometer with a very large bulb. This was 
filled with dry air, which was separated from 
the outside atmosphere by a little pellet of 
mercury in the tube. Knowing the capacity 
of the bulb and the diameter of the tube, the 
percentage increase of volume on heating the 
air through any given range of temperature 
could readily be calculated. The same instru- 
ment may be used as a thermometer. 

If the tube be made of some difficultly fusi- 
ble material, such as hard porcelain, the air 
thermometer serves as an excellent instrument 
for measuring very high temperatures. 

173. Pyrometers. — As mercury boils at 350° 
C, and glass speedily softens, the ordinary 
mercury thermometer can not be used to deter- 
mine high temperatures. We use here a spe- 
cial class of instruments known as pyrometers 
(fire measures), which depend for their action 
upon the expansion of air; the expansion of 
metal bars ; the melting of alloys of known melting points ; 
the softening of fire clays ; or the variable electric resistance 
in a platinum conductor, due to change in the temperature. 
In general the resistance of the metals increases with heat, 
and consequently the current passing through the con- 
ductor becomes weaker the higher the temperature. By 




Fig. 106. 



SOME EFFECTS OF HEAT 163 

measuring the current with a galvanometer we can measure 
the heat. 

174. Range of Temperature. — The lowest temperature so 
far reached is probably —225° C. (what would this be on 
Fahrenheit scale?), obtained by the evaporation of solid 
nitrogen. The highest is probably that of the electric arc, 
which is estimated to be about 3,500° C. Higher and lower 
temperatures than these are entirely conceivable, and un- 
doubtedly exist in other parts of the universe, but they are 
quite outside the range of human experience. 

175. Relation of Temperature to Animal and Vegetable 
Life. — Human life exists within rather narrow ranges of 
temperature, about — 60° F. and + 120° F., and none of us 
care to endure either of these extremes for any great length 
of time. 

Warm-blooded animals keep a constant bodily tempera- 
ture, however much the temperature may vary about them. 
For example, the temperature of the internal organs of a 
human body must be kept at about 98° F., summer and win- 
ter, without change. How this is accomplished will be 
learned later. Some birds keep a constant temperature of 
110° F. The temperature constant varies among different 
types of warm-blooded animals. Birds and mammals (ani- 
mals whose young are fed by the mother's milk) are warm- 
blooded. All other animals are variable in temperature, 
and their temperature varies as that of their surroundings. 
They are sluggish as the temperature falls, and more or less 
active as it rises. 

The distribution of plants and animals over the globe 
appears to be controlled by temperature, so that we have 
certain kinds of plants and animals peculiar \o the tropics, 
certain other kinds peculiar to the temperate zone, and still 
other kinds peculiar to the frigid zones. All three kinds 
of temperature zones may be found upon the slope of a 
single mountain, each to a limited degree supplied with its 
appropriate plants and animals. 



164 PHYSICS 

176. Heat determines the State of a Substance. — A gas 

may apparently be expanded indefinitely, and so may take 
any increase of temperature without changing its state. 
Not so with solids and liquids. The heat may be increased 
to a given point, called respectively the fusing and the boil- 
ing point, but beyond this any further increase of heat 
shows itself by liquefaction and vaporization. 

177. Fusion. — All solids heated to a sufficient tempera- 
ture will melt. We can prove this by direct experiment 
for most solids ; and for others, such as carbon, we believe 
it to be true. Some solids pass directly from a solid to a 
liquid state, as ice, while others pass through an interme- 
diate pasty condition. The latter appears to be the result 
of a change in the molecular structure, and has not yet 
been clearly explained. This pasty condition is important 
practically, since it allows the process of welding. Two 
pieces of wrought iron heated to a white heat may be 
joined together into practically one piece by appropriate 
hammering. 

Sulphur behaves very oddly. Heated at 114.5°, it melts 
to a thin, straw-colored liquid. At from 200° to 250° the 
liquid takes on a rich reddish-brown color and becomes so 
pasty that the test-tube may be turned upside down with- 
out loss. Heated still further, the pasty mass again be- 
comes perfectly liquid, grows darker in color, and finally 
boils at 448.4° and may be distilled. Or if poured into 
cold water and suddenly cooled, it for a time has the appear- 
ance of crude rubber. 

The following laws of fusion apply only to substances 
which show a sharp, distinct melting point : 

1. The fusing temperature, under constant pressure, is 
always the same for the same substance. 

2. The temperature during fusion remains constant 
until the whole substance is melted. 



SOME EFFECTS OF HEAT 



165 



TABLE OF MELTING POINTS. 



Mercury — 39° 

Ice 0° 

Butter and lard 33° 

Phosphorus 44° 

Potassium 63° 

Wax 65° 

Sodium 95° 

Sulphur ■... 110° 

Tin 230° 

Bismuth 262° 

Lead 326° 



Zinc 412° 

Antimony 432° 

Aluminium 600° 

Bronze 900° 

Silver 954° 

Gold 1045° 

Copper 1054° 

Cast iron 1150° 

Steel 1350° 

Wrought iron 1550° 

Platinum 1775° 



178. Change of Volume due to Fusion. — Nearly all solids 
increase in volume when they melt, so that as liquids they 
are less dense, and consequently any unfused portions sink 
to the bottom. With cast iron, water, and bismuth the 
very opposite is the case. They expand at the point of 
solidifying to make room for the crystals which form. 
This force of crystallization is immeasurably great, and, as 
we saw in section 164, is leveling mountains. As a result 
of expansion, these solids are less dense and float on their 
corresponding liquids. Bismuth is added to lead in type 
metal so as to make it expand on solidifying, and fill out all 
the fine lines of the mold. For the same reason iron makes 
fine castings and may be fashioned into delicate patterns in 
stove castings and the like. Metals which do not thus ex- 
pand are made to receive impressions by stamping them with 
dies. Ice, as we all know, floats on water. It has a density 
of only .92, and consequently floats with .08 of its bulk out 
of water. The giant icebergs seen in northern waters have 
11^ times as much ice under water as above. 

179. Change of Fusing Point under Pressure. — The change 
of volume that takes place on fusion makes it easy to 
understand why pressure should change the fusing temper- 
ature. Where a solid expands on fusing, pressure increases 
the amount of work to be done, and hences raises the 



166 PHYSICS 

fusing point; but where the solid contracts on melting, 
pressure diminishes the amount of work to be done, and 
so lowers the fusing point. 

180. Effect of Alloys upon Fusing Point. — In general, 
mixtures of two or more solids melt at a temperature lower 
than their average fusing point, and sometimes less than 
the fusing point of any one of them. Thus an alloy con- 
taining two parts bismuth and one part each of lead and 
tin melts at from 95° to 98° C. A bar of this alloy held in 
a jet of steam melts and drops off like butter. 

181. Vaporization. — Liquids pass to the state of vapor 
by evaporation and boiling. Evaporation takes place at the 
surface only, and proceeds at all temperatures. In boiling, 
the formation of vapor takes place throughout the mass of 
the liquid, and only occurs at a definite temperature, which 
varies with the pressure and the nature of the liquid, but is 
constant for any given liquid under the same pressure. 

182. Five Factors of Evaporation. — The evaporation of 
liquids depends upon five factors : 

1. Temperature of liquid. 

2. Surface exposed. 

3. Pressure. 

4. Amount of vapor already in the atmosphere. 

5. Eenewal of fresh atmosphere. 

A moment's reflection will show this to be the case. 
The hotter the liquid, the more motion will its little par- 
ticles have, and the more able will they be to detach them- 
selves from their neighbors and go off into space. Evapora- 
tion, being a surface phenomenon, takes place in larger 
measure the larger the surface exposed. 

In the chemical laboratory, where we often have occa- 
sion to evaporate solutions, we satisfy these two conditions 
of temperature and surface by using evaporating dishes — 
shallow little porcelain dishes which may be heated over a. 
Bunsen burner. Where we wish the temperature not to 
exceed 100° C, we put the dish on a water bath. The same 



SOME EFFECTS OF HEAT 167 

principles are utilized in drying fruit and other products by 
spreading them out in the sun. 

When a liquid evaporates, its vapor has to make way 
against the overlying atmosphere. Consequently, the 
smaller the pressure, the less work to be done. Where a 
high temperature is undesirable, evaporation is now gen- 
erally carried on in vacuum pans. Our best dried fruits, 
condensed milk, sugar sirups, etc., are evaporated in this 
way. 

The amount of vapor already in the atmosphere deter- 
mines the rate of evaporation, because, as we shall see in 
the next paragraph, a given space can only take up a given 
amount of vapor. For the same reason a renewal of atmos- 
phere furthers evaporation. The weekly wash is hung out 
in the open air to dry, utilizing the heat of the sun, the sur- 
face of the garments, and the renewal of air by the wind. 
In dry climates, as in Colorado, one's collar never " wilts " 
however hot the weather, since the skin always remains dry, 
the perspiration evaporating as soon as formed. 

183. The Evaporation of Solids. — By the term evapora- 
tion we mean, in general, the passage of a liquid to a gase- 
ous condition. But we have also apparently the changing 
of solids to gases without passing through the liquid state. 
Thus snow and ice pass directly into a vapor without the 
visible formation of moisture when the weather is very dry, 
even though the temperature may be below the freezing 
point. Wet clothes hung out upon the line in such weather 
freeze stiff, but the ice will nevertheless disappear from 
them in a few hours. Often after a little rain in winter it 
clears off cold and windy. The moisture upon the sidewalk 
freezes to a thin glade of ice. A dry wind is blowing, and 
the temperature is falling all the time, but in a few hours 
all the ice disappears. In the same way certain volatile 
solids, such as camphor and ammonium-carbonate, are 
greedily taken up by the atmosphere. Under the influence 
of heat other solids, such as iodine and arsenic, pass directly 



168 PHYSICS 

into the condition of vapor, and condense as solids again 
when sufficiently cooled, a process which we distinguish as 
sublimation, the condensed products being called subli- 
mates. But in all these cases we are forced to imagine 
that the solids passed, if only momentarily, through the 
condition of liquid before it reaches the gaseous state, 
since our experience obliges us to conceive of these states 
as continuous. 

184. Vapors. — The amount of evaporation that may take 
place when a liquid is exposed to a given space is almost 
independent of the amount of other gases and vapors pres- 
ent in that space — a condition which is commonly summed 
up by saying that to vapors all space is empty. Under given 
conditions of temperature and pressure, a given space can 
only contain a certain amount of a vapor. When this maxi- 
mum amount is present, the vapor is said to be saturated. 
Below this point the vapor is said to be unsaturated. 
There is no hard-and-fast line between gases and vapors. 
The term gas is usually applied to those bodies, like oxygen, 
hydrogen, and nitrogen, that may be liquefied only under 
very high pressure and at very low temperature, while 
the term vapor is reserved for the gaseous state of those 
bodies, such as water, ether, and alcohol, which under ordi- 
nary conditions exist as liquids. 

185. Critical Temperature. — The greater instrumental 
facilities that have been brought about by the mechanical 
progress of recent years have made many remarkable ex- 
periments possible. Especially has it enabled us to study 
the behavior of gases under great pressure. The old dis- 
tinction of the " permanent gases " has been broken down 
completely, since every one of them— oxygen, hydrogen, 
nitrogen, the atmosphere itself — has been reduced to the 
liquid and even to the solid state. But the temperature 
must always be taken into account. These experiments 
have all been conducted at very low temperatures, under 
conditions therefore which rob the gases of a large part of 



SOME EFFECTS OF HEAT 



169 



their molecular energy. It has been found, for example, 
that carbonic-acid gas (C0 2 ), which can readily be liquefied 
under a pressure of a few atmospheres, can not be liquefied 
at all if the temperature be above 31° C. Below this tem- 
perature, under pressure, the substance becomes a liquid ; 
31° C. is therefore spoken of as the critical temperature for 
carbon dioxide. It is probable that all gases have such 
a critical temperature, above which they can not by any 
amount of pressure be liquefied. 

186. Boiling. — With increasing temperature, vapors exert 
an increasing pressure. As soon as this pressure becomes 
equal to the surrounding' atmospheric pressure, the process 
of boiling takes place, which, as we have seen, is simply the 
formation of vapor throughout the liquid. If water be 
heated in a glass flask, the heat being applied, of course, to 
the bottom of the flask, it will be noticed that the first 
bubbles produced at the bottom of the water collapse before 
they reach the surface. This produces the well-known 
" singing " which is familiar to every watcher of the tea- 
kettle. In spite of the rapid cur- 
rents, the upper layers of water are 
colder than those below, and so 
condense the rising bubbles. When 
all the water is boiling hot, the bub- 
bles reach the surface, and the wa- 
ter boils freely. 

After the water has been boiling 
for some time we shall have all the 
air driven out of the flask, and only 
vapor of water occupying the space 
above the water. If, now, the flask 
be tightly corked and inverted in a 
stand over a suitable trough, we 
may make the water boil again, and quite tempestuously, 
by pouring cold water over the outside of the flask. This 
result is ordinarily so unexpected that it was early named 




Fig 



170 PHYSICS 

the " culinary paradox," but in reality it is very easily ex- 
plained. The cold water chills the flask, and so condenses 
the vapor of water inside. This greatly reduces the pres- 
sure, and consequently the boiling point. Though now 
below 100°, the water in the flask is still highly heated. 
The cold water can not, of course, heat the water in the 
flask up to the ordinary boiling point, but it can and does 
bring the boiling point down to the temperature of the 
water. 

187. Laws of Boiling and Table of Boiling Points. 

1. Under a given pressure, every liquid has a definite 
boiling point. 

2. When the boiling point is reached, the temperature 
remains constant, until the liquid is completely vaporized. 

3. The pressure of the vapor given off during boiling is 
equal to the atmospheric pressure. 

TABLE OF BOILING POINTS. 



Water 100 c 

Alcohol 79 c 

Ether 37° 

Spirits of turpentine 130° 



Sulphuric acid 325° 

Mercury 353° 

Sulphur 440° 

Phosphorus 290° 



188. Changes in the Boiling Point. — The boiling point is 
so characteristic that it is often used, particularly in organic 
chemistry, to determine whether we have to deal with a 
single liquid or a mixture. The same principle is made use 
of in fractional distillation. By keeping the temperature 
constant, the liquids which distill over will be mainly those 
boiling at or under that temperature. Or we may allow the 
temperature to rise at will, and collect the vapors given off 
within certain limits, such as 80° to 85°, 85° to 90°, etc. 
This process is used in separating the lighter constituents — 
benzine, naphtha, etc. — from the heavier oils in crude petro- 
leum. Any change in the composition of a liquid at once 
changes its boiling point. Pure water alone boils at 100° C. 
If mixed with alcohol, the boiling point is lowered. If there 



SOME EFFECTS OF HEAT 171 

are any salts in solution, the boiling point is raised. Com- 
mon salt may be dissolved in water so as to raise the boiling 
point to 102°, saltpeter to 116°, potassium carbonate to 
135°, and calcium chloride to 179°. 

The range in boiling points is very great. Liquefied 
gases boil at many degrees, even hundreds of degrees below 
zero, as liquid oxygen, at — 1 80° C. Light liquids boil below 
100°, as alcohol at 78°, and benzine at 80°. Heavy liquids 
boil at higher temperatures, as mercury at 350°. 

But the greatest change in the boiling point comes from 
variations in the pressure. This is but natural, since boil- 
ing takes place when the vapor pressure equals the atmos- 
pheric pressure. Water boils at 0°, when the pressure is 
reduced to almost nothing. At places much above the sea, 
water boils at so low a temperature as to introduce incon- 
veniences into the kitchen. Eggs and vegetables boiled in 
such water are not sufficiently cooked. Devices are used 
to increase the boiling point by either adding some salt to 
the water or by increasing the pressure artificially. On 
the other hand, where the pressure is greatly increased, as 
in the boiler of a locomotive, the boiling point may even be 
doubled. Under a pressure of 30 pounds the boiling point 
rises to 120° C. ; under 45 pounds, to 134° ; under 60 pounds, 
to 144° ; under 75 pounds, to 152° ; under 90 pounds, to 156° ; 
and under 150 pounds, to 180°. If the pressure upon such 
a body of superheated water be suddenly removed, as by a 
leak, the water bursts into steam, and we have an explosion 
comparable to that of gunpowder. 

The nature of the containing vessel also influences the 
boiling point. Water may be made to boil several degrees 
higher in a glass vessel than in a metal one. Under favor- 
able conditions, we have found this difference as great as 
3° C, and other experimenters have even reported a differ- 
ence of 6°. For this reason, thermometers are standardized 
for 100° by immersion in steam rather than in water. (See 
Fig. 103.) 



172 PHYSICS 

189. Determination of Altitude by Thermometer. — The 

lowering of the boiling point of water by decrease of pres- 
sure furnishes a means of measuring height by the ther- 
mometer. At sea level the boiling point is 100° 0. The 
decrease is not uniform, but in general it may be said that 
a lowering of the boiling point 1° C. indicates an ascent 
of 295 metres, or 538 feet for 1° F. 

Altitude = 295 (100 - t) metres. 

190. Saturation. — A certain volume of air, or the same 
empty space, can hold only a given quantity of vapor. It 
is then said to be saturated. It is found, however, that 
this quantity increases with the temperature, and that the 
maximum quantity is constant only for a given tempera- 
ture. We may express the quantity of vapor present in 
the atmosphere, or in empty space, in three ways : 

1. By stating in grams the absolute weight of the vapor 
present in, say, one cubic metre. 

2. By expressing the relative saturation or humidity — 
that is, the actual vapor present as a percentage of the 
maximum vapor that might be present at that temperature. 

3. By giving the vapor tension. 

191. Vapor in the Air— Dew Point. — The most impor- 
tant application of these principles is found in the measure- 
ment of the water vapor present in the atmosphere, for 
upon this depends so many climatic and hygienic con- 
ditions. So long as the atmosphere is not saturated, and 
is not chilled at any one point, we are only indirectly con- 
scious that there is any moisture present. But if a body 
of moist air suffers a decrease of temperature, the actual 
amount of water vapor remains the same, but the relative 
humidity increases, since the cool air is nearer to its point 
of saturation. If the cooling proceed far enough, the point 
of saturation is reached, and moisture thus formed is known 
as deiv, if it deposit as a liquid film on solid objects ; as 
frost, if it deposit as a solid film of ice ; as cloud, or mist, or 
fog, if it deposit as liquid particles in the air ; or, finally, 



SOME EFFECTS OF HEAT 



173 






as snow, or sleet, or hail, if it deposit as a solid precipitate in 
the air. The temperature at which such precipitation of 
moisture takes place is called the dew point. In dry air, 
the dew point is very low, since the air must be greatly 
cooled before it will deposit any moisture. 
In damp air, on the contrary, the dew point 
is very high, because a slight cooling causes 
a precipitation of moisture. 

192. Humidity. — A variety of instruments 
are used for measuring the amount of mois- 
ture in the air ; among others are the wet- 
and dry-bulb thermometers. 

Two thermometers are mounted on arms 
from the same stand. The bulb of one of 
them is covered with muslin, kept moist by 
a cotton wick leading from a glass of water. 
The constant evaporation from the muslin 
reduces the temperature and makes the read- 
ing of this thermometer lower than that of 
the free one (217). But the rate of evapo- 
ration depends, among other things, upon 
the amount of moisture already present in 
the atmosphere, and the fall in the wet-bulb 
thermometer will' therefore be an indication 
of the hygroscopic condition of the atmos- 
phere. The relative humidity is obtained from specially 
prepared tables. 

193. Rainfall. — The amount of precipitation, or the 
rainfall, is measured in English-speaking countries in 
inches. The annual rainfall is the depth at which the 
total rain would stand had it fallen on a perfectly level sur- 
face and none been lost. It is measured by means of a 
rain gauge, an instrument which collects the precipitation 
over a given area. The water collected is poured into a 
tall measuring glass of small diameter, so that the rainfall 
can be measured to the hundredths of an inch. 



Fig. 108.— Wet- 
and dry-bulb 
thermometers. 



1?4 



PHYSICS 



There are places in the interior of the continent, in 
Death Valley, in the Sahara, and elsewhere, which have no 
rain the year round. The greatest rainfall is supposed to 
be in northern India, at the foot of the Himalaya Moun- 
tains, where it amounts to over 600 inches. In the English 
lake district the rainfall amounts to over 150 inches. It is 
only 24 at London and Edinburgh, yet the prevalence of 
fog makes these cities seem much damper than our own. 
In the United States it varies over a wide range. It is about 
45 inches in our Eastern seaport cities. The following table 
shows the annual rainfall in a number of localities : 



Boston, Mass 44.96 

New York, N. Y 44.80 

Philadelphia, Pa 39.84 

Baltimore, Md 43.95 

Washington, D. C 43.46 

Charleston, S. C 56.74 

New Orleans, La 60.52 

St. Louis, Mo 41.08 

Chicago, 111 34.76 



St. Paul, Minn 27.47 

Denver, Col.. 14.49 

Santa Fe., New Mexico 14.25 

Phoenix, Ariz 7.21 

San Diego, Cal..... 10.51 

Los Angeles, Cal 18.30 

San Francisco, Cal 13.71 

Seattle, Wash 37.44 

Portland, Ore 46.83 



194. Moisture and Health. — The humidity of the air has 
a marked influence on comfort and health. Moisture makes 
the sensations of both heat and cold particularly painful. 
In the dry interior — in Minnesota and Dakota, for example — 
a temperature of —40° F. is not uncomfortable if the wind 
be very light, while in damper Eastern climates a tempera- 
ture of 0° E. chills us through. 

On the other hand, our methods of heating buildings in 
winter make the air too dry for health and comfort. It is 
not the absolute amount of moisture, but the relative amount 
with reference to temperature— the approximation to the 
dew point— that is to be considered for health and comfort. 
We are most comfortable when the moisture in the air is 
from fifty to seventy-five per cent of the amount required 
for complete saturation. Prof. E. De 0. Ward, of Harvard 
University, says our houses in winter have a desert climate. 



SOME EFFECTS OF HEAT 175 

The mean annual humidity at Santa Fe is 44.8 per cent. 
The humidity in our houses in winter time is frequently 
30 per cent, while, at the same time, the humidity out- 
doors may be 71 per cent. 

195. Illustrations. — The air exhaled from the lungs, or 
the " breath," as we call it, is warm and moist ; warm from 
the bodily heat and moist from the evaporation that takes 
place from the internal pores. If the surrounding air be 
cold, the moisture in the breath precipitates as a mist, and 
we have the phenomenon known as " seeing our breath." 
In summer time, the air being more moist then, a glass of 
cold water, or an ice pitcher, becomes covered with dew, and 
some people wonder how the water ever got through the 
glass or the pitcher, but we soon learn that the water did 
not come through at all. It deposited from the surround- 
ing air. This was cooled to the dew point by contact with 
the cold glass or pitcher, and so had to deposit some of its 
moisture. 

On a cool morning in spring or fall, or on a damp morn- 
ing in summer, we find a fine deposit of dew on the grass, 
on cobwebs, stones, boards, and other objects. These cool 
more rapidly than the surrounding air, and so have a lower 
temperature ; hence the deposit of dew. Again, on a damp 
day, a few strokes of the air pump will so far expand and 
cool the air in the receiver that a noticeable mist will be 
produced. 

Tyndall mentions that on one occasion, when a ball was 
in progress at the Winter Palace in St. Petersburg, the 
rooms became overheated, and the outside doors were 
thrown open. The very cold air that rushed in chilled the 
warm, moist air to such an extent that the precipitated 
moisture froze and fell as snow. The same phenomenon 
has been known to take place in large train sheds. The 
hot, moist air from the locomotives, rising into the cold 
air in the upper regions of the sheds, produces a slight 
snowfall. 



176 PHYSICS 

In Nature, the precipitation of moisture is seen on all 
sides. The air directly over a river or lake is moist. When 
this air is chilled by other air currents, the moisture pre- 
cipitates, and often, in the early morning, if one is on top 
of a mountain, the course of a neighboring river can be dis- 
tinctly traced by the serpentine line of fog. A very hot 
day gives rise to generous evaporation on all sides, and the 
afternoon of such a day is apt to see heavy thunder clouds 
and showers. The phenomenon of regular fog precipitation 
is perhaps nowhere better seen than in southern California. 
The air presses eastward across California, to replace the 
hot air of the arid regions in the southeastern part of the 
State and in western Arizona. This air comes off the 
Pacific, and is therefore moist. As it chills, the moisture 
falls out as a heavy fog, which may trail eastward from the 
coast for several miles. 

The same thing is seen in the cloud banners that attach 
to some of the slender mountain peaks in the Alps, such as 
the Matterhorn. The moist air blowing against these cold, 
needle-like summits is sufficiently chilled to deposit its 
moisture. The cloud thus formed trails off from the moun- 
tain as a long, graceful banner, and takes, of course, the 
direction of the wind. Such a cloud may appear constant 
for several hours, although it is continually making and 
unmaking — making at the mountain, and unmaking at the 
end, by dissolving into the air again. 

The formation of dew and frost depends largely upon 
the clearness of the atmosphere. (This will be explained in 
section 203.) On a cloudless, quiet night, the deposit will 
be comparatively heavy. Plants and other objects part with 
their heat more freely on such a night. A very thin covering, 
such as a piece of paper, by preventing the escape of heat, 
will present dew from collecting upon an object. .Note 
that it is not that the paper collects the dew which would 
fall upon the object, but that the paper prevents the object 
from cooling so as to collect dew from the air which touches 



SOME EFFECTS OF HEAT 177 

it. Compare this with the way an ice pitcher collects dew. 
On a cloudy night there is much less deposit, because the 
clouds act as the paper screen. If a wind is blowing, there 
is also less chance for deposit, since the air does not remain 
long enough in contact with the earth to become chilled. 
On cloudy, windy nights, there is rarely either dew or frost. 
196. Condensation, Solidification, and Crystallization. — 
These processes are the opposite of vaporization and melt- 
ing, and are always accompanied by the giving out of heat. 
Any change in matter which makes it more mobile, as 
melting, solution, vaporization, takes in heat ; while any 
change which makes it less mobile gives out heat. (Sec- 
tions 218 and 219.) 



13 



CHAPTEE XX 

' HOW HEAT IS TRANSFERRED 

197. General Statement. — The transference of heat means 
simply the transference of molecular motion from one body 
vibrating with a given intensity to another body vibrating 
with a less intensity. It is a transfer of energy in precisely 
the same way that mechanical reactions are transfers of 
mass energy. There are many ways by which mass energy 
may be transferred from one body to another, as we saw in 
studying machines. There are three ways by which heat 
may be transferred from one body to another — conduction, 
convection, and radiation. 

198. Conduction. — This, although the least effective, is a 
very common way by which heat is diffused. If a stout 
iron wire have one end placed in a fire or other source of 
heat until it become red hot, we notice that the heat ap- 
pears to travel along the wire, and, if the wire is not too 
long, affects the distant end perceptibly. Since the mole- 
cules are not free to move along the length of the wire, but 
are only free to vibrate within very narrow limits, it must 
be that the motion is passed along the wire from molecule 
to molecule, just as a blow may be passed along a line of 
boys, each boy receiving a blow from one neighbor and 
passing it on somewhat diminished (we will say) to the 
neighbor on the other side. We thus have at one end of 
our wire molecules so excited that they are red hot, and at 
the other end molecules that are comparatively cool. But 
two molecules in different states of motion can not exist 

178 



HOW HEAT IS TRANSFERRED 



179 



side by side without an interchange taking place, and some 
movement toward equilibrium. So the tendency is for the 
wire to become equally hot throughout its length, and for 
the stream of heat-motion to continue flowing from the hot 
to the cold end until this equilibrium is brought about. 

If there were no loss of heat, the wire would in reality 
become red hot throughout its entire length* whatever that 
might be. But meanwhile the wire is in contact with the 
cooler air, and must give up its heat to that as well as to 
the colder portions of its own length. Consequently, if the 
wire be long enough, there will be a point where the loss 
and gain just equal each other. Heat will consequently 
flow from the source to this point, and the wire will show 
diminishing heat intensity. Beyond this point the wire 
will have the same degree of heat as the surrounding air. 

"We might define conduction, then, as a transference of 
heat from molecule to molecule, and limited mainly to solid 
bodies. There is slight conduction among the molecules of 
fluids, but the mobility of the molecules makes it possible 
for them to be the direct carriers of heat without passing it 
along molecule to molecule, as in the case of the more rigid 
solids. 

Solids and fluids differ much in their conducting power. 
In genera], the more compact the structure, the greater the 
conductivity. Hence the metals are the best conductors ; 
wood and stone are poor conductors, and fibrous materials, 
such as fur, felt, and cloth, which contain many air spaces, 
are bad conductors. The best conductor we have is silver ; 
the worst conductor, air. The following table arranges the 
metals in order of diminishing conductivity relative to 
silver : 



Silver 1.000 

Copper 736 

Gold 532 

Brass 231 

Zinc 190 



Iron 119 

Steel 116 

Lead 085 

Platinum 084 

Bismuth 018 



180 PHYSICS 

There are many practical ways of showing the different 
conducting power of the metals. Thus wires of different 

metals are fastened in- 

Fig. i09.-Conduction. the projecting ends. 

When boiling water is 
poured into the box, the unequal melting of the wax shows 
the unequal conductivity of the metals. 

Liquids are very poor conductors. A test tube full of 
water may be made to boil in the upper portions, while the 
lower portions are quite cool. 

199. Applications. — There are hundreds of daily applica- 
tions of these principles. The non-conductors are used either 
to keep heat out or to keep it in. In the former case, as in 
ice-houses, the walls are made of brick, straw, sawdust, 
ashes, etc., and serve to keep out heat. But more frequently 
non-conductors are used to keep the heat in. In buildings, 
both of brick and of wood, a hollow air chamber is allowed 
between the outer and the inner walls, since, as we have 
seen, air is the poorest conductor. For the same reason, 
double windows keep out the cold, not so much by guarding 
us from currents of air as by interposing an air chamber. 
The same principles obtain in our clothing. Loose, fibrous 
materials and loose garments are warmer than close, tight- 
fitting goods. Flannel blankets are warmer when new, and 
before the fibers have been closely matted together. The 
Norwegian cooking box is another application. It is made 
of wood and lined with felt. A covered metal pail, con- 
taining water and the joint of meat boiling hot, is placed 
inside the cooking box, and the whole carefully closed. 
The loss of heat is very slow, and the cooking process goes 
on for several hours without the application of any addi- 
tional outside heat. 



HOW HEAT IS TRANSFERRED 181 

The furnace in the basement for heating houses is mere- 
ly a large iron stove, around which a wall of brick is built to 
prevent the heat from passing out into the cellar. If it is 
a " hot-air " furnace or a " hot-water heater," its heat is 
carried to all parts of the building by a process to be dis- 
cussed in the next section. If it is a " steam-heater," its 
heat is stored, distributed about the building, and recovered 
by processes to be discussed in sections 213 and 218. The 
ducts which carry the hot air, hot water, or steam about the 
building are incased in brick walls, where that is possible, 
to prevent the loss of their heat in transmission. Where 
these ducts pass through the open basement, they are some- 
times covered with non-conducting material of loosely 
woven hair or felt. Wrapped with this covering, steam 
pipes are frequently carried long distances underground 
to heat remote buildings. In comparison with other mate- 
rials, the earth is not a very bad conductor, and yet con- 
duction is such a poor method of diffusing heat that, as 
has already been said, although heat so intense exists be- 
neath the surface as to fuse the rocks, yet that heat does 
not penetrate to the surface sufficiently to effect a rise in 
temperature of one thirty-sixth of a degree. 

Water pipes are laid a few feet underground to prevent 
them from freezing in winter— that is, the earth is a suffi- 
ciently poor conductor to prevent the heat from passing out 
of the water to such an extent that it may freeze. (It is 
better to state it thus, than to speak of cold passing in 
through the earth to the pipes ; just as we speak of light 
coming into a room through a window, but do not speak 
of darkness doing the same.) We should remind ourselves 
that all things have some heat, and that when things grow 
cold they are simply losing some of their heat. 

We sometimes ride in an open carriage in the coldest 
weather and are quite comfortable, because we wrap our- 
selves in what we call warm clothing and blankets. We 
sleep in cold rooms comfortably, or may be even too hot, 



182 PHYSICS 

under our "warm" blankets. Now, they are not warm at 
all — indeed they are just the temperature of all other 
things around them, so that if we wrap a thermometer up 
in " warm " clothes or blankets it will not show the least 
bit of rise in temperature. In order that our ideas may 
be clear we should use some other word than warm to 
describe these coverings. What we need is some word like 
non-conducting, which would imply that they keep the 
heat of our bodies from passing off. Our bodies generate 
at all times a great deal more heat than we need. It is 
only necessary that we regulate the outflow of this heat so 
that the temperature of our vital organs may be . always 
about 98° F., night and day, summer and winter, at work 
or at rest. 

The chemical action, which, as was said in section 160, 
produces heat in piles of green grass, new hay, piles of oily 
cotton waste, etc., is very slow and produces very little 
heat per hour, but these substances are such poor conduc- 
tors that the heat is not allowed to pass off, and it is pos- 
sible for it to accumulate until it reaches the kindling tem- 
perature of the substance, when " spontaneous " combustion 
will take place. 

Snow protects vegetation in winter from killing frosts. 
It must be remembered that solutions do not freeze as 
readily as pure water, and therefore the juices of plants 
will not freeze at 32° F. While the snow can not enable 
the plants to rise above that temperature, it does prevent 
them from falling much below it ; among other reasons, 
because being filled with air spaces it is a very poor con- 
ductor. 

200. Convection. — This practically means the transfer of 
heat by the transfer of the heated body itself. Fluids are 
heated almost entirely by this process. If we consider the 
heating of water in a teakettle, or, better still, in a glass 
beaker, where we can see what is going on, we shall notice 
that the whole fluid is in a state of constant motion. A 



HOW HEAT IS TRANSFERRED 



183 





Fia. 110.— Convection. 



little sawdust in the water will make the action plainer. 
The source of heat is under the beaker (Fig. 110), and the 

bottom is naturally the hot- 
test part. The water di- 
rectly in contact with this 
becomes heated, expands, 
and in so doing grows light- 
er. The colder, heavier wa- 
ter, therefore, presses down 
under this and buoys it up 
toward the surface. As soon 
as this becomes cooled and the other hot, another overturn- 
ing occurs, and so the process goes on until the whole mass 
of water is heated to the boiling point, if the source of heat 
be intense enough, or to the point where loss and gain of 
heat just balance. In the same way a stove or a steam radi- 
ator warms the air of a room. The air is such a poor con- 
ductor that we should be badly off if we had to depend 
upon its passing along the heat to us by conduction. In 
reality, the air in contact with the stove or radiator becomes 
heated and is buoyed 
up by colder, heavier 
air. 

This is illustrated 
by Fig. 111. We may 
think of the air in 
the pasteboard box as 
a pair of scales with 
columns of air of 
equal weight stand- 
ing upon either scale 
pan. A candle is 
lighted at the bottom 

of column a, which expands it and drives a portion of the 
air out. What remains is no longer heavy enough to bal- 
ance the weight of the column b, and it pushes down and 





V 




X&mJh 


| 






'f 




i 
a 


'■S 


b 






Ji 


\ ( 


1 * 




z^m 


} [ 


/\ 




/ 



Fig. 111. — Convection. 



18J: PHYSICS 

forces a movement of air through the box and up «, which 
continues as long as the heat is supplied by the c.andle. 

The upper part of a room is warmest and may be many 
degrees above the air near the floor. We notice it very 
plainly if we have occasion to climb up on a stepladder to 
hang a picture. If we set the door of a room ajar, we may, 
by means of a candle flame, show that currents of air (cold 
air) are coming in at the bottom and currents of air (warm 
air) are going out at the top of the door. 

If a room is to be ventilated by the windows, the best 
way is to make a small opening at both top and bottom, 
since this promotes convection currents. 

This principle of convection is of the utmost impor- 
tance in Nature. It is the great source of movement in the 
atmosphere. The unequal heating of the air above land 
and sea creates our so-called land and sea breezes. The 
greater heat at the tropics causes the air there to expand, 
and in consequence the colder air from polar latitudes 
pushes in and takes its place. This action, combined with 
the earth's daily rotation, is the source of those permanent 
air movements known as the trade winds. 

The heating of water by convection, and the resulting 
convection currents in oceans and lakes, are great equal- 
izers of temperature the world over. By convection we 
heat the water in the kitchen boiler from the stove. By a 
similar process houses are heated by hot water. The hot- 
air furnace is dependent upon convection to convey its 
heat over the house ; and many methods of ventilation 
depend upon this way of promoting air currents. 

201. Radiation. — This third process of transferring heat 
is different from either conduction or convection. It is so 
closely allied to the propagation of light that we shall con- 
sider it at length when we come to take up the mechanics 
of the ether. We shall discuss it here rather briefly. 

Consider how we get heat from a fire on the hearth. 
Evidently it is not brought to us by conduction, for air 



HOW HEAT IS TRANSFERRED 185 

is almost an absolute non-conductor. Neither can it reach 
us by convection, for all the air currents move from us 
toward the fireplace, and up the chimney. Indeed, it is 
found that the heat would reach us quite as well, and even 
better, if there were no air or any other substance between 
us and the fire. The sun, and every other heated body, 
appears to give off heat in all directions throughout space. 
Yet we believe that heat, being molecular motion, can not 
exist apart from matter, and consequently we think it can 
not be transmitted as heat through space. Space reacts as 
if it were filled with some medium, neither gaseous nor 
liquid, but having some properties of a solid. The more 
we study the phenomena of space, the more we seem com- 
pelled to assume that all space is filled with a very tenuous 
medium called the ether, which is capable of transmitting 
a variety of wave motions, some of which beget heat, some 
light, and some electrical phenomena, upon reaching the 
earth. Hot bodies are supposed to be able, by means of 
molecular motions, to set up vibrations in the ether, and the 
ether is capable of setting up molecular motions in bodies of 
matter. Heat transferred by radiation is supposed, there- 
fore, to be transferred by a wave motion of the ether. It is 
called radiant heat, because it goes out in all directions 
through space in straight lines or radii, which have their 
center in the heated body. This wav # e motion has a velocity 
of about 186,000 miles per second, and for such distances as 
we have to deal with on the earth, may be considered in- 
stantaneous. 

All matter with which we are acquainted radiates ether 
waves, because all substances have some heat — that is, mo- 
lecular motion ; so that every portion of matter is radiating 
heat to every other portion of matter. The hotter ones 
radiate more abundantly than the cooler ones, and thus 
tend to bring about a state of equilibrium. Moisture in 
the air converts ether waves into heat. If we go up into 
the upper regions of our atmosphere, either upon a moun- 



186 PHYSICS 

tain top or in a balloon, where there is scarcely any moist- 
ure, we find that the sun's rays produce intense heat in us, 
but the air about us is, nevertheless, extremely cold. Tyn- 
dall says : " A joint of meat might be roasted before a fire 
with the air around the joint as cold as ice. The air on 
high mountains may be intensely cold, while a burning sun 
is overhead ; the solar rays which, striking on the human 
skin, are almost intolerable, are incompetent to heat the 
air sensibly, and we have only to withdraw into perfect 
shade to feel the chill of the atmosphere. I never, on any 
occasion, suffered so much from solar heat as in descend- 
ing from the ' Corridor ' to the Grand Plateau of Mont 
Blanc, on August 13, 1857. Though Mr. Hirst and myself 
were at the time hip-deep in snow, the sun blazed against 
us with unendurable power. Immersion in the shadows of 
the Dome du Goute at once changed our feelings, for here 
the air was at freezing temperature. It is not, however, 
sensibly colder than the air through which the sunbeams 
passed ; and we suffered, not from the contact of hot air, 
but from radiant heat, which had reached us through an 
icy cold medium." 

A hot body, by .its molecular motion, sets up ether 
waves. These ether waves may be sent through a lens cut 
out of ice and focused upon paper, there to set up those 
molecular motions which we call heat and set fire to the 
paper. It was heat in the radiating body, and it became 
heat again in the body or bodies which received it, but it 
was not heat in passing. 

202. Absorption, Radiation, and Reflection. — When ether 
waves impinge upon matter, one or more of three things 
must happen : 1. They may be transmitted without pro- 
ducing any effect upon the substance. This not only hap- 
pens with dry air, but it may also happen with certain 
liquids, and even* solids. 2. They may be reflected wholly 
or in part. 3. They may set up molecular motions (heat) 
in the substance, wholly or in part. This is called absorp- 




JOHN TYNDALL (1820-1893). 
Succeeded Faraday as professor in the Royal Institution of Great Britain. No 
man has done more hy his lectures and writings than he to disseminate science. 



HOW HEAT IS TRANSFERRED 187 

tion. The law of the conservation of energy obtains here. 
Suppose we put a glass screen between us and the fire, and 
that ninety per cent of the radiant energy which falls upon 
the glass is converted into heat, then the remaining ten per 
cent must be accounted for as transmitted or reflected. It 
must also be remembered that all of the ninety per cent 
which was converted into heat will, by molecular motions 
in the body, set up again an exactly equivalent amount of 
ether vibration and then radiate off again. The power to 
arrest ether waves and convert them into heat varies much 
with different substances. A piece of zinc will protect 
woodwork from the heat of a stove better than a sheet of 
asbestos can do it, because the zinc reflects back most 
of the ether waves which strike it, while the asbestos con- 
verts a very large portion of them into heat and will scorch 
the paint or the wood underneath it. Indeed, the thinnest 
coating of metal, like gilt lettering, will protect wood from 
the heat of the stove, while ordinary paint, no matter what 
color, so far from protecting it, converts the ether waves 
into heat and scorches the wood. For this reason water in 
a clean metal dish before the fire will not heat as rapidly 
as water in a metal dish that has been smoked or coated 
with varnish, enamel, etc. In the first case the waves 
which come to the dish are reflected, and in the second 
case they are converted into heat and raise the tempera- 
ture of the water. If hot water is poured into these two 
kinds of vessels, its heat will radiate out from the coated 
metal vessel faster than from the other, and a thermometer 
will show a more rapid loss of temperature. In general, 
those forms of matter whose molecules are most readily set 
in motion by the ether waves (good absorbers) are best 
capable of setting up ether waves by their molecular 
motions (good radiators). 

203. Relation of Heat and Light.— When we watch an 
iron ball slowly heated until it gives out light — first a dull 
red and afterward a bright light — we very naturally are led 



188 PHYSICS 

to suspect that heat and light are closely akin to one 
another. This we shall find to be true when we study 
light, and we shall then learn in what their kinship consists. 
It is sufficient at present to say that it is analogous to the 
relation which exists between sounds of low pitch and 
those of high pitch. The sun sends us both kinds of ether 
waves — those which give us the sensation of light and 
those which give us the sensation of heat. One is readily 
converted into the other. Dry air is perfectly transparent 
to both kinds of rays, but the moisture of our atmosphere 
absorbs most of the heat-producing rays. The moisture 
radiates this heat in all directions, and thus a large portion 
of it passes off into space again without ever reaching the 
earth. Waves which give us the sensation of light pass, 
without much loss, through the air to the earth, where they 
are partly reflected again into space, but for the most part 
are absorbed and converted into heat. This heat sets up 
ether waves of the heat-producing kind which would pass 
off into space if the moisture of the air did not arrest them, 
absorb them, and radiate a portion of them back again. 
Thus it will be seen that the moisture of our atmosphere 
acts as a sort of valve to entrap sunlight and warm the 
earth. What the moisture of the air is to the earth, the 
glass is to the " hot bed " in the garden, or the glass roof 
to the greenhouse. Indeed, the same thing is true in a 
measure of a shingle roof, or any kind of cover, as for 
example an umbrella ; for, however opaque these coverings 
may appear to the eye to be, they are in reality transparent 
to a large number of the rays which come from the sun 
and produce heat in objects upon the earth ; but these same 
coverings are opaque to the rays which these warm objects 
upon the earth send out, and they prevent them from pass- 
ing off again into space. A covering of snow protects the 
crops in the same manner that a " hot bed " protects young 
plants ; although it can not raise the temperature above 
32° F., it does prevent it from falling below that degree, 



HOW HEAT IS TRANSFERRED 189 

and there are many plants to which this temperature is not 
injurious. 

Because different substances differ in their power of 
radiating, no two things are likely to be of the same tem- 
perature. This is why dew and frost collect more upon 
some things than upon others, and they thus tell us which 
things are the best radiators. It should be noted that dew 
and frost collect more upon the grass than upon the bare 
ground. Which of these spots is, therefore, the best ab- 
sorber of the sun's rays ? From which will a thin layer of 
snow disappear sooner? Why does earth sprinkled upon 
snow melt away the snow from underneath it ? 

In Sahara the cold at night and the heat by day are 
equally painful to bear. Whenever the climate is dry the 
daily range of temperature is great. This is the marked 
difference between mountainous or interior climate, and 
that by the sea or other bodies of water. 

A piece of paper will prevent the loss of heat from a 
plant during the night, so that a thermometer may stand 
10° higher under the paper than outside. 

The clouds act like this paper screen, and hence we 
have more dew or frost at night when the sky is clear than 
when it is overcast. Indeed, a thermometer will rise and 
fall at night as a cloud is passing over. 

A thermometer resting on the grass at night has been 
found to be 14° lower than one suspended four feet above it. 

Painted metals will collect more dew than bright metals. 
This is merely a question of temperature, as the thermom- 
eter will show. 

204. Radiometer. — This consists of a glass globe from 
which nearly all the air has been removed. A light vane, 
made of tiny mica plates mounted on an aluminium frame, 
is so arranged that it is free to rotate on the steel pivot in 
the center of the globe. One face of each mica plate is 
darkened with lampblack. When the radiometer is exposed 
to radiant energy coming from the sun, or from a cup of 



190 



PHYSICS 



hot water, or the warm hands of a person, the little vane 
begins to rotate, spinning the more rapidly as the radia- 
tion is greater. The darkened 
- faces absorb more heat, and 

J the straggling air particles 

:',, ' : >ti A coming in contact with these 

] faces are themselves heated 

-7; -- and fly off. The reaction 

sends the vane in the opposite 
direction, and so it spins on 
its pivot, the darkened face 
in the rear. If a tin cup be 
smoked on one side, filled 
with hot water and held near 
the radiometer, we may show, 
by turning the cup about, that 
the blackened side radiates 
more heat than the bright 
metal side. We may now 
cover the bright metal side 
with white paint and show 
that it radiates as well as 
lampblack. The power to 
absorb is always equal to the power to radiate, and the 
white paint absorbs heat-radiation as readily as lampblack 
does, but this is not true for light-radiation, of which, as 
we know, the white reflects more. 




Fig. 112.— Eadiometer. 



CHAPTEE XXI 

CALORIMETRY AND SPECIFIC HEAT 

205. Measurement of Heat. — Heat, like all forms of en- 
ergy, is a measurable quantity. The process of measuring 
heat is one of great scientific and practical importance. 
We may measure either of the two aspects of heat that we 
have mentioned, either its degree or its amount. We call 
the first measure Temperature, and the second Quantity. 

206. Temperature. — This, as we have seen, corresponds 
in mass-mechanics to velocity or rate of motion, and is 
quite independent of the amount of matter in motion. In 
heat-mechanics temperature is the degree of molecular 
motion, and is also quite independent of mass. 

As temperature can not be directly measured in C.-G-.-S. 
units, we are forced to devise some conventional and quite 
empirical unit, and to make our measurement consist 
merely of a statement of relative intensity. This we do 
with a thermometer (167). 

207. Quantity of Heat, as we have seen, corresponds in 
mass-mechanics to momentum. It is not only the degree 
of heat, the temperature, but it is also the amount of mat- 
ter heated. It is evident that although a cup of boiling 
water is hotter than a ten-gallon tank of lukewarm water, 
the tank has a greater quantity of heat and will do more 
toward warming a cold room. So it is evident that a great 
lake at a temperature of 40° F., although it is not hotter, 
yet it contains more heat than a cup of boiling water, and 
will do more to modify the winter climate of that region 

191 



192 PHYSICS 

than many thousand cups of boiling water could. The 
relation of temperature to quantity of heat is analogous to 
the relation of water pressure to volume of water. The 
mountain stream may exhibit high pressure of water ; the 
quantity may, however, be too small to be useful. We can 
not measure quantity of heat in C.-G.-S. units, and so must 
devise an empirical unit. The Calorie is our name for 
such a unit. It is the quantity of heat needed to raise the 
temperature of 1 gram of pure water 1° C. It is a mere 
convention. We might use 1 kilogram, or 1 pound, or 1° F., 
and often do, but this unit is, on the whole, the most 
convenient. 

208. Specific Heat. — As soon as we come to measure 
temperature and quantity of heat, we come upon a very 
characteristic and important difference in the behavior of 
bodies toward heat. If we take a kilogram of water and a 
kilogram of some metal such as lead or mercury, and raise 
the temperature of water and metal the same number of 
degrees, we find that it takes a different and much larger 
amount of heat to increase the temperature of the water 
than that of the metal. We express this by saying that 
different bodies have different capacity for heat. As water 
absorbs a great amount of heat in changing its temperature 
by a given number of degrees, we say that water has a great 
capacity for heat. We measure the heat capacity of any 
body by comparing it with the capacity of water. We call 
the ratio Specific Heat, which we may define as the heat 
capacity of a given mass of a substance compared with the 
heat capacity of the same mass of water. 

209. Determination of Specific Heat.— There are several 
methods in use for the determination of specific heat. 

The method of mixtures is the one generally used, and 
is the only one suitable for elementary work. In this 
method we heat a known mass of the body to a definite 
temperature, say 100° C, and then plunge it into a known 
mass of water whose temperature is also known. The tern- 



CALORIMETRY AND SPECIFIC HEAT 193 

perature of the water is generally taken at that of the room, 
and consequently rises when brought into contact with the 
hotter body. The water is well stirred, and when the tem- 
perature ceases to rise, the hot body and the water must 
have reached the same temperature. The increase in the 
temperature of the water multiplied by its weight in grams 
gives the quantity of heat imparted to the water by the cool- 
ing body. The heat gained by the water and the heat lost 
by the body are manifestly equal. The total number of 
heat units given out by the cooling body, divided by the 
number of degrees of fall in temperature, gives the amount 
of heat for each degree, and this amount divided by the 
number of grams of weight in the body gives the amount 
of heat yielded by each gram as it falls one degree. Since 
the temperature of the vessel containing the water, as well 
as that of the water itself was raised, its heat capacity must 
also be taken into account. 

The case will be made clear by an example. Suppose 
we take 100 grams of water in a copper cup weighing 12 
grams, both at the temperature of the room, which is 17.5° 
degrees. From a vessel of boiling water we lift a piece of 
lead weighing 100 grams and put it into the copper cup of 
water. We stir the lead about, so that it and the water 
may become of the same temperature, and when the tem- 
perature becomes stationary we find it is 20°. The lead 
has given out heat enough to raise 

100 grams of water 2.5 degrees = 250 heat units, and 
12 grams of copper 2.5 degrees = 12 X 2.5 X.0933* =2.8 

heat units. 
Total number of heat units given out by the lead = 252.8 

in falling 80 degrees. 

Amount given out for each degree ^M _ 3 16 heat 
units. 80 



* See table on the following page for specific heat of copper. 
14 



194 PHYSICS 

Amount given out by each gram for each degree of fall 
in temperature =■ — — = .0316. If one gram of lead gives 

out .0316 heat units in falling one degree, it would require 
.0316 heat units to raise one gram of lead one degree. This 
is called the specific heat of lead. In accurate work, allow- 
ance must also be made for the heat capacity of the ther- 
mometer, and for the loss of heat by radiation ; but we 
neglect these, and still get fair results. 



TABLE OF SPECIFIC HEATS. 



Water 1.000 

Aluminium 212 

Iron .■ 114 

Copper 093 

Tin 056 

Silver 057 

Mercury . . 033 

Gold 032 



Platinum 032 

Lead 032 

Glass .019 

Sulphur 203 

Graphite 218 

Charcoal .241 

Ice 504 

Alcohol 610 



210. Applications. — Among liquids, water has the largest 
specific heat, and this is of immense importance in the 
economy of Nature. Water acts everywhere as an equalizer 
of temperature. It has such great capacity for heat that it 
warms up slowly and cools down slowly. Hence the cli- 
mate near large bodies of water is much less subject to 
extremes of temperature than places surrounded by land. 
The movement of large bodies of hot water from the 
tropics to the poles, and of cold water from the poles to the 
tropics, make habitable large areas of land that would 
otherwise be lost to human uses. The Gulf current 
greatly moderates the climate of the British Islands and of 
the northwest coast of Europe, while the Japan current 
performs the same service for the northwest coast of 
America. 

The kitchen range may be much hotter than the water 
in the hot-water tank which is connected with it, but if the 



CALORIMETRY AND SPECIFIC HEAT 195 

fire goes out on a cold winter night the warm water in the 
tank will give out its heat all night long and perceptibly 
warm the room, while the stove will have parted with its 
comparatively small amount of heat in a very short time. 

The summer sun beats alike upon the seashore and the 
adjacent waters of the sea, but the specific heat of sand 
being much less than that of water, its temperature rises 
much higher than the water. The air over the water will, 
therefore, be cooler than that over the land, and will press 
toward the land, giving a " sea breeze." At night the land, 
like the kitchen range, will lose its heat sooner than the 
water does, and the air over the land will become cooler 
than that over the sea, and will press toward the sea, giv- 
ing a " land breeze." 



CHAPTER XXII 

LATENT HEAT 

A. Heat disappeaks when Solids liquefy 

211. Heat latent in Solutions. — If we apply heat to some 
fragments of ice, the temperature rises until the whole 
stands 0° C. The ice then begins to melt, but though the 
application of heat be continued, no rise of temperature 
takes place until all the ice has melted and passes into wa- 
ter at 0°. The heat applied during this interval has accom- 
plished no change in the temperature, but has been solely 
spent in changing the ice at zero into water at zero. Evi- 
dently a large quantity of heat has disappeared in the pro- 
cess. We say that it has become latent. It has been em- 
ployed to do internal work among the molecules, and is in 
the form of potential energy. All this heat may be recov- 
ered again, as we shall see in section 219. 

Common salt put into water will cause its temperature 
to fall several degrees. It abstracts heat from the water, as 
it dissolves or passes into the liquid state. This heat does 
not raise the temperature of the salt, but becomes latent. 
This is true of all solids when they dissolve. 

Each solid has its own peculiar power of rendering heat 
latent. Ice, for example, absorbs 80 heat units for each 
gram liquefied. And it is a physical impossibility for ice 
or snow — any form of water in the solid state — to pass into 
the liquid state without its absorbing this amount of heat ; 
but ice and snow do not take heat very readily by either 
196 



LATENT HEAT 197 

conduction or radiation, and this explains why they linger 
so long even under a hot sun. Every one must have some- 
times wondered that a cake of ice will endure for so long a 
time the broiling summer's sun, and that snow will some- 
times last until late in spring. 

212. Freezing Mixtures. — When we want only a moder- 
ate cold, as in the case of drinking water, the ice is simply 
dissolved in water. When the ice melts, we have, of course, 
water at 0° C. as the immediate result, but we also have the 
original drinking water greatly cooled, since the ice, to melt, 
must take its heat of liquefaction, 80 calories per gram, 
from the surrounding water. So it is possible, by using 
little water and much ice, to keep the contents of a water 
pitcher at 0° C. for a considerable time, since the ice can 
melt only as it can absorb the requisite heat from the sur- 
rounding water. 

When a greater cold is wanted, as in freezing creams and 
fruits and ices, it is gained by mixing salt with the cracked 
ice. The action is double — the melting of the ice and the 
solution of the salt — and both processes require heat ; that 
is, are cold-producing. The salt (sodium chloride, NaCl) 
has a great affinity for water. We express this by saying 
that it is deliquescent. We all know how damp table salt 
becomes if exposed to the air on a moist day. So strong is 
this affinity that the salt melts the ice in order to dissolve in 
the water formed. But, in order to dissolve, the salt must 
itself absorb its own heat of liquefaction, and so contribute 
its share to the production of cold. It is possible in this 
way to obtain a temperature as low as — 22° C. 

The act of solution is always accompanied by a lowering 
of the temperature. If we take a mixture of solid ammo- 
nium chloride (XH 4 C1) and ammonium nitrate (NH 4 N0 3 ) 
and place them in a beaker, and then add just enough cold 
water to dissolve them, we shall have a temperature consid- 
erably below zero. This can be shown by stirring the mix- 
ture with a chemical thermometer and noting the reading, 



198 PHYSICS 

or, better still, by using a small test-tube with a little water 
in the bottom, as a stirrer. The water will be frozen 
solid, and may be turned out on the table as a transparent 
lump. 

The faculty of salt to liquefy ice is made use of to re- 
move ice from the pavements in cold winter weather. It 
liquefies the ice, although it makes it colder than it was be- 
fore. We should, therefore, avoid saying it melts the ice. 
The salt solution which is formed flows off and clears the 
pavement. It does not freeze until a very low temperature 
is reached. 

B. Heat disappeaes when Liquids yapoeize 

213. Heat latent in Vapors. — When we supply heat to 
water its temperature rises constantly until it reaches 100° 
C, and here a halt takes place until all the water at 100° 
has been converted into steam at 100°. The heat mean- 
while has been spent in changing the water into water 
vapor. Evidently a large quantity of heat has disappeared 
in the process, and yet all this heat may be recovered again, 
as we shall learn in section 218. We therefore say that it 
has become latent. When water or any other liquid changes 
its state, passing from liquid to gas, heat is apparently used 
up in producing this change of state. Each liquid has its 
own peculiar power of rendering heat latent. Water, for 
example, absorbs 537 heat units for each gram vaporized. 
It is not possible for water or any other liquid at any tem- 
perature to pass into the vapor state unless it is supplied 
with the number of heat units required to bring about that 
change. That is, 1,000 grams of water (about 1 quart) 
must absorb 537,000 heat units before it can vaporize. 
This shows why a little shower on a summer day, whose 
water quickly evaporates, cools the earth so much. 

Those who have seen experiments with liquid air must 
have marveled that the liquid does not fly away into the 
gaseous state more readily than it does. This is because it 



LATENT HEAT 199 

is unable to appropriate to itself the necessary amount of 
heat to change its state. 

In general, we may say that when substances pass to a 
more fluid state — solids to liquids, liquids to gases, gases in 
expanding — heat is absorbed, and that when substances 
pass to a less fluid state — gases in condensing, gases to 
liquids, liquids to solids — heat is given out. For the same 
substance, the amount of heat absorbed in any given change 
is precisely the same as the amount given out when the 
change is in the opposite direction. 

214. Absolute Temperature. — We have called attention 
to the fact that temperature is analogous to velocity in 
mass-mechanics. But velocity may diminish until it finally 
ceases altogether, and the body comes to rest. If the anal- 
ogy were complete, there would be a corresponding point 
in the thermal scale where molecular activity would cease, 
and the body be devoid of all heat. Such a condition would 
be absolute cold, or the absolute zero of temperature. It has 
never been attained experimentally, but we can estimate it. 

If a body of air at 0° C. be chilled to —1°, or heated to 

+ 1°, its volume will change by — of its original volume 

at 0°. If, therefore, we should heat it to +273°, its vol- 

273 

ume would increase by rrr of its original volume. That is, 

its volume would just double. If, now, we should cool this 

273 

body of air to —273°, it ought to shrink — of its original 

volume, and therefore cease to have any volume whatever. 
Before reaching that temperature, however, every gas would 
become liquid, and cease to follow Boyle's law. This point, 
— 273° C, we call the absolute zero. 

We may construct a scale of absolute temperature by 
referring all readings to the absolute zero. We can readily 
do this in the centigrade scale by simply adding 273° to 
all ordinary readings. Thus all readings in absolute tern- 



200 PHYSICS 

perature must be positive. Water freezes at 273° and boils 
at 373°. 

215. The Production of Cold.— Cold is the absence of 
heat, and is simply relative. It means a lower degree of 
molecular energy. Cold is produced, therefore, by the 
reversal of all those processes which are the sources of heat. 
However, it is not practically possible to reverse all of them, 
such as solar radiation, mechanical motion, and electricity. 
Nor can we, except in rare cases, make chemical reaction a 
source of cold. The reverse of chemical combination — that 
is, chemical decomposition — requires the taking in of heat, 
but the process is not self-promoted and can not, therefore, 
be used as a source of cold. Practically we are thrown back 
upon three sources for the production of all artificial cold — 
expansion of gases, evaporation of liquids, and the dis- 
solving of solids. 

216. Expansion of Gases. — This is a very effective source 
of cold, but it is rarely used in the arts, because there are 
more convenient methods. It usually appears, indeed, as 
an inconvenience. Motors driven by compressed air be- 
come very cold, and consequently brittle, by the expansion 
of the air in the cylinder. It is sometimes the custom to 
surround parts with running water in order to equalize 
temperatures. The cold produced by expanding air may 
be beautifully seen in the receiver of an air pump. On a 
damp day a few strokes of the pump suffice to fill the 
receiver with fog, a precipitation of moisture due entirely 
to the chilling effect of expansion. 

In Nature, the expansion of air in the upper regions of 
the atmosphere is a source of considerable cold, and is 
probably one reason why the higher clouds are made up of 
tiny ice crystals instead of globules of condensed water 
vapor. Whatever be the cause of this fall in temperature, 
it amounts to about 1° for each 300 feet of elevation. 

217. Cold by Evaporation. — This is the great source of 
artificial cold, and also one of the most convenient in way 



LATENT HEAT 201 

of application. It has already been incidentally referred 
to (192). 

Whenever a liquid evaporates, it must take in its own 
heat of evaporation, and so make surrounding objects cold. 
In ordinary evaporation, the heat is supplied from some- 
what wide territory as rapidly as it is needed, but by 
increasing the rate of evaporation and shutting out exter- 
nal sources of heat, we may produce very intense arti- 
ficial cold. 

Eemembering the five factors upon which evaporation 
depends, it will readily be seen that we can not well use the 
first, temperature, since that would be fatal to our purpose, 
but we can use the other four conditions. We can increase 
the surface, we can diminish the pressure, we can remove 
the vapor as fast as it is formed by pumping or by con- 
stantly renewing the atmosphere. 

The porous water jars of the East depend for their 
cooling action upon the large surface exposed, and the 
renewal of atmosphere which comes when the jars are hung 
in a good draught of air. They are made of unglazed 
earthenware, and consequently the water makes its way 
through the pores to the surface, and by evaporation cools 
the water still in the jar several degrees below that of the 
surrounding air. The experiment may be made by using 
the porous cup of a battery, and either placing it in a good 
draught of air, or directing a jet of air against it from a 
bellows or pump. 

The Carre Ice Machine, one of the oldest, depends on 
the evaporation of liquefied ammonia gas, KH 3 . Under 
ordinary conditions NH 3 is a gas, but under a pressure of 
seven atmospheres it becomes a colorless liquid which boils 
at —33.7 C. The liquefied gas is passed through coils sur- 
rounding the body of water to be frozen. By simply remov- 
ing the pressure the XH 3 passes back to the gaseous state, 
and in doing so absorbs enough heat to reduce the temper- 
ature of surrounding objects to something below zero. 



202 PHYSICS 

The ammonia gas may be again liquefied, and so used over 
and over again with little loss. The ice is thus made at 
the cost of the mechanical energy used in liquefying the 
ammonia. 

The most intense cold is produced by the evaporation of 
much more difficultly liquefiable gases, such as carbon diox- 
ide, C0 2 , and even the elementary gases N and 0. By the 
evaporation of N, a cold of — 225 0. has been attained. 

The value of bathing the forehead with cologne or bay 
rum, in case of headache or fever, comes from the cooling 
effected by the evaporation of the alcohol. 

A simple application of evaporation, in freezing water, 
is an ice machine, consisting merely of an air pump pro- 
vided with a chamber containing strong sulphuric acid, 
H 2 S0 4 . A flask, half filled with water, is connected by 
means of a rubber stopper and tube with the acid chamber 
and the pump. A few strokes of the pump remove most of 
the air from the flask, and under the reduced pressure the 
water begins to evaporate very rapidly. But the H 2 S0 4 has 
strong affinity for water vapor, and absorbs it so rapidly 
that it re-enforces the air pump in maintaining a vacuum, 
and so hastening the evaporation of the water in the flask. 
Under this greatly diminished pressure, bubbles of vapor 
form throughout the mass of the liquid, so that it boils at 
a very low temperature. But, meanwhile, the rapid evap- 
oration of the water has been carrying off so much heat 
that a film of ice begins to form on the surface, while the 
water below continues to boil. We have thus the spectacle 
of water boiling and freezing in the same vessel and at the 
same temperature. When the flask is brought on the table, 
those not in the secret naturally wonder how such a large 
sheet of ice got into such a small-necked bottle. 

This experiment may be made with the ordinary air 
pump by introducing into the receiver a vessel containing 
strong H 2 S0 4 and another containing water. It was in this 
form that the experiment was originally made by Leslie. 



LATENT HEAT 



203 




Fig. 113.— Wollaston's 
Cryophorus. 



Wollaston's Cryophorus (Fig. 113) illustrates the same 
principle. It consists of a U-tube with a bulb at each end. 
One bulb is half filled with water, and 
the other bulb and the tube itself with 
vapor of water. When this second bulb 
is surrounded by cracked ice, the water 
condenses, and thus reduces the pres- 
sure inside the tube. The water in the 
other bulb rapidly evaporates, and crys- 
tals of ice are seen to form on the sur- 
face. 

If two large watch crystals be moist- 
ened on their convex sides and placed 
on top of each other, with some highly 
volatile liquid, such as ether, placed in the upper crystal, it 
will be easily possible to freeze the two crystals together by 
the rapid evaporation of the ether. This may be brought 
about by simply blowing on its surface, or by directing an 
air jet against it from a bellows. 

Still another instance. The cold produced by evapora- 
tion may be readily observed by dipping the bulb of a 
chemical thermometer into ether or chloroform, or even 
into alcohol or water, and rapidly swinging it in the air ; 
or by wetting a cloth with one of these liquids, wrap- 
ping the cloth around the bulb, and then swinging the 
thermometer as before, or directing a blast of air against 
the cloth. 

Besides these applications, there are numerous other cir- 
cumstances where we wish an intense cold. In engineering 
work it is now the custom to freeze " quicksands " by 
means of liquefied ammonia gas, XH 3 . A tunnel or shaft 
can be driven through this solid mass of sand and water, 
when it would be quite impossible to deal with the semi- 
fluid, shifting quicksand. 

A freezing cold is also used in microscopic work in 
studying delicate organic structure that must be cut into 



204 PHYSICS 

sections thin enough to allow the light to pass through. It 
is so used in the Department of Agriculture at Washington 
in investigating diseases of domestic animals. The heart, 
liver, or kidney, or whatever organ is under examination, 
is first frozen stiff, and then, by means of a sharp razor, a 
wonderfully thin section is sliced off and mounted between 
little glass slides before it has a chance to melt and become 
unmanageable. 

All volatile liquids, such as alcohol, ether, benzine, etc., 
feel cold to us. Yet the liquids are not cold, except when 
they are allowed to evaporate. 

The water bath in the laboratory and the double boiler 
in the kitchen are used because the evaporation of the wa- 
ter will absorb all heat above a certain temperature, and 
prevent the " burning " of the food, etc. Upon the moun- 
tain top, where the pressure of the air is reduced, evapora- 
tion proceeds more rapidly, and it may abstract heat to such 
an extent as to prevent cooking, by boiling water, of certain 
things which require a temperature of at least 100° C. 

All animals produce more heat than they need. Their 
life processes depend upon the elimination of superfluous 
heat. This is absorbed chiefly by the evaporation of moist- 
ure produced from countless pores in the skin. Cold con- 
tracts the surface blood vessels and sends the blood to the 
interior of the body where it will not lose so much heat, 
but it also contracts the mouth of these pores — as evidenced 
by the so-called " goose pimples "—checks the flow of per- 
spiration, and thus evaporation and the consequent loss of 
heat are reduced. Heat causes the surface blood vessels 
to relax and the warm blood to flush the skin where it 
cools. Heat also opens the pores, causes the perspiration 
to flow, and if the conditions of evaporation are favorable, 
we do not suffer with the heat. If, however, there is great 
humidity in the atmosphere, so that evaporation does not 
proceed readily from our bodies, we suffer greatly from the 
heat, and we callit a " muggy " day. 



LATENT HEAT 205 

C. Heat reappears when Vapors liquefy 

218. Heat recovered from Vapors. — When any gas passes 
to the state of a liquid, its latent heat is given out. If the 
gas be steam, then the liquid must be water, and each gram 
of condensed water at 100 represents the liberation of 537 
calories. This method of heat production is illustrated in 
our steam radiators. The condensing steam yields its heat 
to the^ iron radiator, and this in turn to the apartment. 
In ^Nature, the liquefaction of vapor is a most important 
source of heat. Whenever the moisture in the atmosphere 
coudenses into rain or snow, heat is liberatedo Conse- 
quently, precipitation is always accompanied by rise of tem- 
perature. We notice a moderation of the weather during a 
rain. It has been calculated that the moist air accompany- 
ing the Gulf Stream yields as much heat to Great Britain, 
by the precipitation of the moisture, as is brought by the 
Gulf Stream itself. 

D. Heat reappears when Liquids solidify 

219. Heat recovered from Solutions. — The freezing of 
water requires the giving up of the exact amount of heat 
required to liquefy the ice, 80 calories for each gram, and is 
a most important natural source of heat. Farmers under- 
stand this, and put tubs of water in their vegetable cellars 
on a cold night, so that if the temperature falls below 32° 
F. the freezing of the water will give out such quantities of 
heat as shall prevent the temperature from falling far below 
32°, and the vegetables will not freeze until a temperature 
considerably below 32° is reached. Ponds and lakes, by the 
freezing of their waters, do much toward preventing the 
temperature of the immediate neighborhood from falling 
far below 32° F. For the same reason the atmosphere is 
genial and agreeable during a quiet snowstorm. 

220. Recapitulation.— Suppose 1,000 grams of ice at —10° 
C. rises to 0°. The specific heat of ice being .5 (209), this 



206 PHYSICS 

would require the absorption of 5,000 heat units. Next let 
us suppose this ice to melt. This would require 80 X 
1,000 == 80,000 heat units. If now we heat this quart of 
water to the boiling point, 100 x 1,000 = 100,000 heat units 
will be absorbed, and if we vaporize this water, 537 X 1,000 = 
537,000 heat units will be required. Thus a total of 722,000 
heat units have been absorbed, and will all surely be restored 
to the atmosphere before that water can again become ice at 
—10° C. So it appears that water is the great equalizer of 
temperatures, carrying the summer heat far into the winter 
to modify its climate, and storing the winter cold (if we 
may use the expression) with which to refresh the summer 
season. 




MICHAEL FAEADAY (1791-1867). 

Professor thirty-four years in the Royal Institution of Great Britain. Induction 
of electric currents. Effect of magnetism upon polarized light. "The greatest 
experimental philosopher the world has ever seen." A superior lecturer. 



MAGNETISM AND ELECTRICITY 



CHAPTER XXIII.— Magnets 

221. Magnetite. Fig. 114. 

222. Steel Magnets. 

223. The Poles of a Magnet. Fig. 115. 

224. Magnetic Substances. 

225. Influence of Magnets upon Magnetic Substances. Fig. 116. 

226. Each Molecule a Magnet. Figs. 117 and 118. 

227. The Earth a Magnet. Figs. 119, 120, 121, and 122. 

228. The Mariner's Compass. Fig. 123. 

229. The Law of Inverse Squares. Fig. 124. 

230. Lines of Magnetic Force. Figs. 125, 126, 127, 128, and 129. 

CHAPTER XXIV.— Static Electricity 

231. Electrification. 

232. Two States of Electrification. 

233. Static Electricity and Electric Currents. 

234. Conductors. Fig. 130. 

235. Induction, the Influence of Electrified Bodies upon Neighboring 

Objects. Figs. 131 and 132. 

236. By Induction a Polarized Body may receive a Charge from a 

Neutral Body. Fig. 133. 

237. The Electrophorus. Figs. 134, 135, 136, and 137. 

238. Condensers. Figs. 138 and 139. 

239. Lightning. 

240. Electrical Distribution— Effect of Points. Figs. 140, 141, 142, 

and 143. 



CHAPTER XXV.— Electric Currents 
I. Generators of Electric Currents 

241. Sources of Electric Currents. Fig. 144. 

242. Electric Potential. 

243. The Voltaic Cell. Fig. 145. 

207 



208 PHYSICS 

244. The Electro-Chemical Series. 

245. Local Action and Polarization. 

246. Some Typical Cells. Figs. 146, 147, 148, and 149. 

247. The Battery of Cells. Figs. 150, 151, 152, and 153. 

II. Some Effects of Electric Currents 

248. Electric Currents recognized by their Effects. 

249. Physiological Effects. 

250. Thermal Effects. 

251. Chemical Effects. Figs. 154, 155, and 156. 

252. Magnetic Effects. Figs. 157, 158, 159, 160, 161, 162, 163, 164, 165, 

166, 167, 168, and 169. 

III. Electrical Measurements 

253. The Problem of Measurement. 

254. Ohm's Law. 

255. The Tangent Galvanometer. Figs. 170, 171, 172, and 173. 

256. Resistance. Figs. 174, 175, 176, 177, and 178. 

257. Arrangement of Battery Cells. Figs. 179, 180, 181, and 182. 

258. Divided Circuits. Fig. 183. 

IV. Induction 

259. Methods of Induction. 

260. Induction by a Magnet. Fig. 184. 

261. Induction by Varying Currents. Fig. 185. 

262. Direction of Induced Currents. 

263. Strength of Induced Currents. 

264. The Induction Coil. Fig. 186. 

265. Spark Coil and Electric Gas Lighting. Fig. 187. 

266. The Telephone. Fig. 188. 

267. Transformers. 

V. Electric Currents by Mechanical Means 

268. The Magneto-Electric Machine. Fig. 189. 

269. The Dynamo. Figs. 190 and 191. 

VI. Electric Currents produced by Heat 

270. Thermo-Electric Currents. Figs. 192 and 193. 

271. The Thermopile. 



CHAPTER XXIII 



MAGNETS 




221. Magnetite. — There is found in various parts of the 
earth an iron ore composed of oxygen and iron (Fe 3 4 ), which 
will attract small bits of iron. This is called magnetite 
to indicate that it is a magnet. It has also been called 
loadstone for reasons which will appear later. The small 
pieces of iron do not cling to all parts of it alike. If a 
piece of the ore is rolled 
about among filings of 
iron, most of them will 
fall away from the piece of 
ore when it is lifted, but 
many will be found cling- 
ing to two spots (Fig. 114) 
situated upon opposite 
sides or opposite ends from 

one another. A straight line connecting these two parts is 
called the axis, and the ends of this line are called the 
poles of the magnet. It is not necessary that the poles be 
the ends of the lump. They may be anywhere along the 
sides, but it is true that they are always opposite to one 
another. If we suspend the piece of magnetite by a slen- 
der thread, it will come to rest with the same one of these 
poles always north. Let us mark this pole with the letter 
X and call it the north pole, and the opposite portion we 
will call the south pole. Because of this property of point- 
ing north, it was originally called loadstone, or the leading 
15 209 



Fig. 114.— Majmets. 



210 



PHYSICS 



stone. The reason for its pointing north and south will 
be given in section 227. 

222. Steel Magnets. — If either pole of the magnetite is 
rubbed several times upon a steel sewing needle, always 
in the same direction, from one end to the other, the sew- 
ing needle will be found to have acquired the property of 
attracting iron filings at its two extremities. It has become 
a magnet. Its two ends are the poles, and they will point 
north and south if free to move. 

223. The Poles of a Magnet. — If the needle is suspended 
by a thread, so that it may swing freely in a horizontal 

plane (Fig. 115), it will be found 
that the pole of the magnetite 
which was used to magnetize this 
needle will attract the pole of the 
needle which it touched last, but 
will repel the other. It will also 
be found that the opposite pole 
of the magnetite will repel this 
pole of the needle but attract the 
other. If a second sewing needle 
be magnetized in the same way as 
the first (let us suppose that the 
north pole of the magnetite is 
used in each case, and that it is 
drawn from the eye toward the 
point of each needle), it will be 
found that the points of these needles repel each other, 
and that the ends containing the eyes repel each other, but 
that the point of each will attract the eye of the other. 
The law is : unlike poles attract, and like poles repel. It 
will be found that if these needles are allowed to swing 
freely, without being influenced by any magnet, they will 
arrange themselves so that their eyes will point north. It 
will also be found that their eyes will attract the south 
pole of the magnetite but repel the north pole of the same ; 




Fig. 115. — Magnetized needle. 



MAGNETS 211 

also that their points will attract the north pole of the mag- 
netite, but repel its south pole. The poles of these needles 
may be reversed by rubbing them in the opposite direction 
with the same pole of the magnetite as was used before, or 
by rubbing them in the same direction with the opposite 
pole of the magnetite. These sewing needles are small 
" bar magnets." 

The bar magnets which are on sale have the letter N 
stamped upon one end of them. If a bar magnet is free to 
move, this end will point north. If it is brought to the 
north pole of the magnetite, or the north pole of the sew- 
ing needles mentioned above, it will repel, while it will 
attract the south pole of the same. The reverse is true of 
the south pole of the bar magnet. Steel magnets are often 
given the shape of a horseshoe, so that the force of both 
poles may be applied to the same object. 

224. Magnetic Substances. — While a large number of 
substances are affected to a slight degree by very power- 
ful magnets, only steel and iron are visibly affected by mag- 
nets of ordinary strength. Soft iron may be magnetized, 
but will not retain magnetism. The harder the iron, the 
longer it will retain its magnetism. This is why steel, 
which is iron hardened by carbon, makes the most perma- 
nent magnets. Since both poles of a magnet attract mag- 
netic substances, the way to determine whether a magnetic 
substance has become a magnet is to find whether there is a 
repulsion between any part of it and either pole of a magnet. 

225. Influence of Magnets upon Magnetic Substances. — A 
magnetic substance when brought near to a magnet is itself 
always polarized — that is, converted into a magnet. The 
harder the substance the less this action takes place ; but, 
on the other hand, the more permanent is the result. Soft 
iron is readily magnetized and as readily loses its magnetism. 

If a horseshoe magnet (Fig. 116) is brought near to a 
bar of soft iron, even though they do not touch, the iron 
will become a magnet, as will be shown by the way bits of 



212 



PHYSICS 




Fig. 116.— Horse 
shoe magnet po 
larizing soft iron 



iron, as carpet tacks, will cling to it. With a magnetic 
needle we may learn that the bar of soft iron is polarized so 
that its north pole is opposite the south 
pole of the horseshoe magnet, and its south 
pole opposite the north pole of the mag- 
net. As soon as the horseshoe magnet is 
removed the bar of soft iron loses its mag- 
netism, or, at least, retains too little to be 
recognized by ordinary means. A power- 
ful magnet will reverse the poles of a weak 
magnet if like poles are presented to each 
other ; for this reason students should be 
careful about bringing magnets near to 
compass needles which are not free to 
move. 
226. Each Molecule a Magnet. — To enable us to appre- 
ciate what may take place in the needles when we magnet- 
ize them, let us arrange some coarse steel filings in a row 
upon a sheet of paper and draw the north pole of a magnet 
underneath the paper from left to right. The magnet po- 
larizes each small sliver of steel as it passes by, so that the 
end of the sliver nearest to the north pole of the magnet 
becomes a south pole and 
the more remote end of 
the sliver becomes a north 
pole. The repulsion be- 
tween like poles and the 
attraction between unlike 
poles causes each sliver in 
turn to rise up on end 
and turn a somersault — the 
south pole of the sliver al- 
ways turning toward the 
north pole of the magnet (see Fig. 117). The result is that 
after the magnet has passed, the slivers are all arranged in 
line along its pathway with each north pole pointing toward 




Fig. 117. — A magnet polarizing 
steel filings. 



MAGNETS 213 

the left, and inasmuch as they are steel they retain their 
magnetism, the whole mass of filings acting as a solid har 
of steel would — as the sewing needles referred to in section 
223 — having the pole which is like the one used for indu- 
cing magnetism at the end first approached, and the unlike 
pole at the end last approached hy the inducing magnet. 
This we think may be analogous to what happens when a 
bar of steel is magnetized by rubbing it with a magnet, 
each molecule behaving as these slivers of steel do. By 
tapping the paper upon which the steel filings are arranged 
(Fig. 117), after the influence of the magnet has been re- 
moved, they will again become disarranged, so that the 
mass will no longer exhibit north and south poles. So, by 
hammering a steel magnet, its magnetism is made to disap- 
pear. Heating, twisting, bending — anything which might 



Fig. 118. — New poles formed by breaking a magnet. 

tend to disarrange the molecule — weakens a magnet. If 
one of the magnetized needles mentioned in section 223 be 
broken into little pieces — never so small — each piece will 
have a north and south pole, just as the steel slivers men- 
tioned in the early part of this section ; and if the eye of 
the needle is north pole, the end of each small piece of 
needle which pointed toward the eye will be its north pole. 
If the needles could be broken up into molecules, we sup- 
pose that each molecule would exhibit the same kind of 
polarity. Fig. 118 helps us to imagine how the small par- 
ticles may be arranged with reference to each other. This 
explains why the iron filings do not cling to the middle 
portion of the magnet. There the north and south poles 
neutralize each other, while at the ends they are free to 
act. The molecules of iron and steel are assumed to be 
magnets at all times. When they fail to exhibit it they are 
merely disarranged, and when we magnetize iron or steel 
we simply cause its molecules to take the proper arrange- 



214 PHYSICS 

ment. The molecules of iron appear to move more freely 
than those of steel, hence it is more readily magnetized 
and more easily loses its magnetism. If a piece of steel is 
hammered or heated while under the influence of a magnet, 
greater magnetism will be induced in it, as though some 
such assistance were needed to help move the molecules. 
When iron is strongly magnetized its length is slightly 
increased. A faint crackling noise is heard when iron or 
steel are very powerfully magnetized or demagnetized. If 
it is magnetized and demagnetized in rapid succession, the 
metal grows hot, which indicates molecular motion. 

227. The Earth a Magnet. — If we lay a bar magnet upon 
the table under a magnetic needle (Fig. 119), the needle 
will arrange itself so that its south pole will be over the 
north pole of the bar magnet, and its north pole over 
the south pole of the bar magnet. The axis of the needle 
will always be parallel with that of the bar magnet, what- 
ever direction that may take, showing that the force of the 

bar magnet is greater than 
that which tends to cause the 
needle to point north. We 
have reason to believe that 
the earth is a great magnet, 
although not a powerful one. 
Its magnetic axis is in the 
same general direction with 
its geographical axis, and its 
magnetic poles are in the arc- 
tic and antarctic zones. The 
north magnetic pole of the 
earth must be unlike the north pole of our needle, because 
they attract. For this reason it has been proposed to call 
the end of the needle which points north the north-seeking 
pole, but the custom of calling it the north pole persists. 

If we suspend a magnetic needle so that it is free to 
swing in a vertical plane (Fig. 120), and move it about 



Fig. 119. — Magnetic needle. 



MAGNETS 



215 



over a bar magnet, its north pole will point downward 
when it approaches the south pole of the bar magnet, and 
its south pole will dip when it approaches the north pole 
of the bar magnet. The dipping 
needle is affected by the earth as 
by a bar magnet. In the vicinity 
of the equator it hangs horizontally. 
As it is moved north, its so-called 
north pole dips until finally it 
stands vertical over a point north 
of North America, but some dis- 
tance from the geographical north 
pole, as will be seen by reference to 
Fig. 121. Likewise, the magnetic 
south pole does not coincide with 
the geographical south pole, as may 
be seen by reference to Fig. 122. 
From this it is evident that the 
magnetic needle mounted so as to 
swing horizontally does not point 
exactly north and south. Its deviation from that direction 
is called its declination. 

Figs. 121 and 122 show the lines of equal declination, 
and the lines of equal dip, or inclination, as it is called, for 
the whole earth. These figures also show how much the 
magnetic equator differs from the geographical equator. 
The magnetic poles of the earth are gradually shifting their 
position, so that these figures are not correct for all time. 

The table below gives the declination and the inclina- 
tion of the needle at various places for the present year, 
1900. The table also gives the intensity of the magnetic 
force at these various places relative to New York. The 
absolute force of the earth's magnetism at New York, as 
expressed in the C.-G.-S. system, is .61 dynes— that is, a force 
sufficient to move .61 grams 1 centimetre in a second, or 1 
gram .61 centimetres in a second. 




Fig. 120.— Dipping needle. 



216 



PHYSICS 




Fig. 121. — Northern Hemisphere. 



TABLE OF MAGNETIC DECLINATION, INCLINATION, AND 
INTENSITY FOE 1900- 





Declination. 


Dip. 


Intensity relative to 
that of New York. 


New York 


9° 12' W. 

4° 35' W. 
16° 42' E. 
29° 24' W. 
16° 16' W. 
14° 30' W. 

9° 30' W. 
10° 0' W. 

0° 30' E. 


70° 6' N. 
70° 18' N. 
62° 20' N. 
58° 2' S. 
67° 9' N. 
64° 55' N. 
66° 43' N. 
58° 0' N. 
70° 46' N. 


1.00 


Washington 

San Francisco 

Cape Town 


.98 
.89 
.59 


London 


.77 


Paris 


.77 


Berlin 


.79 


Rome 


.74 


St. Petersburg 


.79 



MAGNETS 



217 




Fig. 122.— Southern Hemisphere. 



The declination, dip, and intensity are all gradually 
changing. The following table exhibits the change in 
declination at London for three hundred years : 



d. 1580 


.... II 3 17' E. 


A. D. 1816 


... 24° 30' W. 


1622 


... 6° 12' E. 


1868 


. . . . 20° 33' W. 


1657 


. ... 0° 0' 


1880 


. . . . 18° 40' W. 


1705 


9° 0' W. 


1890 

1900 


. 17° 26' W. 


1760 


. . . . 19° 30' W. 


. . . . 16° 16' W. 



228. The Mariner's Compass. — This is merely a magnetic 
needle free to move in a horizontal plane. It is attached 
to the underside of a card (Fig. 123). This is inclosed in 
a box called the binnacle. A fixed line shows the direction 
of the keel of the ship, while the card, being carried about 



218 



PHYSICS 



by the compass needle, shows always the deviation of the 
ship's course from a north-and-south direction. TJiis devia- 
tion is measured in " points," each point being 11^ degrees. 
Of course it is necessary for the mariner to correct his 




Fig. 123. 



reading for the declination of the needle, which he must 
determine from tables and charts. 

The mariner's compass appears to have been used by 
the Chinese in very crude form long before it was known 
to the Western world. It was discovered independently in 
Europe, perhaps in the twelfth century, but it took several 
centuries for it to reach its perfection. It is difficult to 
estimate the great value it became in the fifteenth century 
in enabling mariners to extend the boundaries of the known 
world. 

From the fact that the earth is a magnet, we might 
expect to find that it would induce magnetism in magnetic 
substances, and this we find to be true. This accounts for 
the magnetism of the ore called magnetite. A compass 
needle brought near to the base of an iron pillar will have 



MAGNETS 



219 



its south pole attracted ; if it is carried to the top of the 
pillar, its north pole will be attracted. From the fact that 
the inclination of the dipping needle is over 70° in New 
York, we might expect to find that the bottoms of iron 
pillars would become south poles by the induction of the 
earth, and such is the fact. Thus it happens that no mag- 
netic substance is ever entirely free from magnetism. 

229. The Law of Inverse Squares. — The magnetic force, 
like gravitation, heat, light, and electric attractions and 
repulsions, varies inversely as the square of the distance. 
Fig. 124 explains this. The force proceeding from F in 
all directions as the radii of a circle, would produce a cer- 
tain effect at «, and only one quarter of that effect at c, 
which is twice the distance of a ; and one ninth the effect 
at c\ which is three times the distance of a ; and one six- 
teenth the effect at c" , which is four times the distance of 
a. The areas at c, c\ and c", being respectively 4, 9, and 
16 times as great as that of a (see Geometry), the force 
must distribute itself accordingly ; but these numbers are 
the squares of 2, 3, and 4 respectively ; hence if we square 
the distances to be compared, we shall get the rate at which 




Fig. 124. — Law of inverse squares. 



these forces diminish at those distances. The usual form of 
statement is: Hie force varies inversely as the square of the 
distance. 

This helps us to answer the question, Why should a sliver 
of iron move toward a magnet ? The magnet polarizes the 



220 



PHYSICS 




Fig. 125. 



sliver of iron, so that the pole of the sliver nearest to the 
pole of the magnet is unlike it, and therefore they attract 
each other ; the farther pole of the 
sliver is like the pole of the magnet, 
and therefore they repel each other. 
But the attraction is greater than the 
repulsion, because the pole which at- 
tracts is nearer than the pole which 
repels, hence the object, if light, and 
if very near, is moved toward the 
magnet. 

Note that magnets in order to exert any large force 
must be very near to the magnetic substance. 

230. Lines of Magnetic Force. — Fig. 125 shows how lines 
of force go out from the pole of a magnet. Figs. 126, 
127, 128, and 129 show how these lines are affected by the 
proximity of other poles. These lines of force may be 
mapped out upon paper by placing the magnet underneath 
and distributing slivers of iron over the surface. Each 
sliver will become polarized and act like a small magnetic 
needle. A fuller illustration, 
however, will be obtained by 








V:.':''h 



Fig.. 126. 



Fig. 127. 



moving a small compass around in the vicinity of magnets 
placed as in the figures. By means of the compass needle 



MAGNETS 221 

we get the lines in three dimensions of space, rather than 
in the one plane alone of the paper. 

We shall learn in the chapter upon Current Electricity 
that these lines of magnetic force may exist without a mag- 
net. We speak of the region penetrated by these lines of 
force as a magnetic field, and we are able to produce, by 
means of electricity, a magnetic field without the presence 
of any magnetic substance. If soft iron be brought into 
this field, produced by an electric current, it becomes a 
magnet, as when brought near a steel magnet. We speak 





Fig. 128. Fig. 129. 

of it then as an electro-magnet. This subject will be 
treated more fully under Electricity (Chapter XXV). The 
reasons for the earth being a magnet will also be found 
there. 

Lines of magnetic force penetrate with perfect ease 
through any substance except iron. The experiments rep- 
resented by Figs. 117 and 125-129 would not be success- 
ful if sheet iron were used instead of paper. Glass, wood, 
or anything else may be used, provided it is thin, so as to 
allow the magnet to come very near to the iron filings. 



CHAPTER XXIV 

STATIC ELECTRICITY 

231. Electrification. — Experience teaches ns that in cold 
weather many things are easily electrified : one's hair, when 
it is brushed ; a cat's fur, when it is rubbed ; a rubber pen- 
holder or comb, when dropped upon the floor; our own 
bodies, when we rub our feet upon the carpet. The elec- 
trification is shown by attraction and repulsion of light ob- 
jects, crackling sounds, and sparks. All bodies are capable 
of being electrified, under proper conditions, and any ob- 
ject which is electrified exhibits attraction and repulsion 
for all other forms of matter. In this respect electricity 
appears to be very unlike magnetism, which affects iron 
alone. The objects which we choose as suiting best our 
purpose for experiment are sealing wax and glass. We get 
the best results when we rub the sealing wax with flannel 
and the glass with silk. Pith balls are chosen for the ex- 
periments, simply because they are very light, and there- 
fore move more readily under the influence of the slight 
forces with which we deal. It is well to gild the pith balls 
for reasons which will appear in section 234. 

232. Two States of Electrification. — Pith balls which have 
been electrified by contact with the electrified sealing wax 
repel each other, likewise pith balls which have been- elec- 
trified by contact with the electrified glass repel each other ; 
but pith balls which have been electrified, one by contact 
with the sealing wax, and the other by contact with the 
glass, attract each other. The law is : Bodies with like 

222 



STATIC ELECTRICITY 223 

kind of electrification repel, those with unlike kinds attract. 
We prefer to speak of kinds of electrification rather than 
kinds of electricity, because we do not believe there are two 
kinds of electricity. We shall speak of glass as being posi- 
tively electrified, and sealing wax as negatively electrified. 
The flannel which is rubbed upon the sealing wax becomes 
positively electrified, and the silk which is rubbed upon the 
glass becomes negatively electrified. Pith balls, when they 
come in contact with an electrified body, acquire the same 
kind of electrification as that body. The way to determine 
whether a body is electrified, or which kind of electrifica- 
tion it may have, is to present it to pith balls electrified 
with each kind ; repulsion, not attraction, determines the 
matter. One's hair " flies " when brushed in cold weather, 
because bodies having like kind of electrification repel each 
other. 

233. Static Electricity and Electric Currents. — The titles 
of Chapters XXIV and XXV, Static Electricity F , and Elec- 
tric Currents, are not intended to convey the impression 
that there is more than one kind of electricity, but that 
electricity may manifest itself in different conditions. The 
present chapter treats of electricity in a state of tension. 
The analogous term in water pressure is hydrostatic, which 
refers to the pressure of water at rest. But electricity may 
flow, and we have conductors for it. Whether the flow of 
electricity through a conductor is like that of water, or like 
that of heat, we may not, at this point, discuss intelligently. 
Chapter XXV treats of Electric Currents, but their con- 
sideration must also enter, to a slight extent, into this 
chapter. 

234. Conductors. — In Fig. 130 b c represents a copper 
wire attached at either end to silk threads a b and c d. 
At e two pith balls are suspended upon silk threads, and 
at / two pith balls are suspended by very fine copper wire. 
Before the experiment begins, the pith balls at / hang in 
contact with one another, as those at e. If now we touch 




224 PHYSICS 

an electrified body to any part of the copper wire b c, the 
electricity flows through the copper wire to the pith balls 
at /, and, each having the same kind of electrification, they 
repel, as represented in the figure. Copper is a conductor 

of electricity. Dry silk is 
d not a conductor ; or, as we 
say, it is a wow-conductor. 
Hence the pith balls at e 
do not separate, because 
they are hung upon silk 
threads. The silk threads, 
a b and c d, are used to pre- 
FlG 130 vent the electricity from 

flowing away from the pith 
balls at /. They are called insulators — another word for 
non-conductors. If we moisten either a b or c d, the pith 
balls at f will fall together again, showing that the elec- 
tricity flows away through moist silk. If the silk threads 
which suspend the pith balls at e are moistened, while a b 
and c d are dry, an electrified body touching b c will cause 
the pith balls at e to separate, as well as those at /. There 
are no perfect conductors, and there are no perfect insu- 
lators ; hence electricity leaks away from all electrified 
bodies, and it is difficult to keep them charged long. Dry 
air is a very good insulator, but the moisture in the air is 
a good conductor. Hence these electrical experiments work 
best in cold weather when there is less moisture in the air. 
It is well to remember that the moisture of the breath may 
interfere with our experiments. 

A telegraph wire is a conductor of electricity, and the 
glass knobs upon telegraph poles are insulators. 

In the table which follows, the best conductors are at 
the head of the list. Electricity produced by friction will 
force its way quite readily through all those in the first 
half of the list. They may, therefore, all be called con- 
ductors, although they differ very widely among themselves 



STATIC ELECTRICITY 225 

in this respect. Copper conducts more than a million 
times as well as water. Those in the last half of the 
list may be called insulators, the poorest conductors being 
at the end of the list : 



Copper. 


Paper. 


Iron. 


Air. 


Carbon. 


Silk. 


Dilute sulphuric acid. 


Sealing wax. 


Water. 


Glass. 


Human body. 


Ilard rubber. 


Linen. 


Porcelain. 


Cotton. 


Shellac. 


Wood. 





The chief difference between electricity produced by 
friction, as in this chapter, and that produced by chem- 
ical action, as in the next chapter, is that although fric- 
tion produces exceedingly small quantities of electricity, it 
is vastly more capable of pushing its way through resist- 
ance ; and hence some things which are called conductors 
in this chapter will be considered insulators in the next. 
Only the first four substances mentioned in the above list 
will be considered good conductors in the next chapter, 
and only the last six are to be considered really good in- 
sulators in this chapter. 

We may now see why we chose sealing wax and glass. 
It is because, being good insulators, they retain their elec- 
trification, while metals and other conductors lose their 
electrification as fast as it is produced. This, however, 
may be obviated by putting glass handles upon metals. 
Of course, the electricity spreads all over the metal sub- 
stance, while with a non-conductor it remains in those parts 
where it is produced. This may be shown by rubbing seal- 
ing wax or hard rubber, in spots, with flannel, and then lay- 
ing it upon some granulated sugar. It will pick up the 
sugar on those spots only which have been rubbed. It will 
now appear why we proposed to gild the pith balls in sec- 
16 



226 PHYSICS 

tion 231. The electricity will thus flow all over the sur- 
face, and they will carry a much larger charge. Dry pith 
is a poor conductor. 

235. Induction, the Influence of Electrified Bodies upon 
Neighboring Objects. — Electrified bodies, like magnetized 
bodies, exert an influence upon objects near them. One 
difference, however, is that an electrified body exerts its 
influence upon all kinds of matter alike ; whereas magnets 
effect iron only. In the case of both magnetism and elec- 
tricity, we believe that the power to influence objects with- 
out contact is due to the ether, which, by its waves, may 
produce heat, light, electric and magnetic 
phenomena. Indeed, many think that 
electricity is the ether. 

When an electrified body is brought 
near any neutral substance, wdthout touch- 
ing it, that substance is, as we might say, 
polarized. The part nearest to the elec- 
trified body exhibits the opposite kind of 
electrification, and the more remote part 
* exhibits the same kind of electrification 

as that of the inducing body. This ap- 
parent action at a distance is known as induction. It is 
not, however, action at a distance, but action through the 
medium of the ether. 

We may now see why there is an attraction between 
neutral bodies and electrified bodies, and why, if either of 
them is very light and free to move, they will come to- 
gether. Fig. 131 represents an electrified stick of sealing 
wax held near to a pith ball, which it has not yet touched. 
Its influence polarizes the pith ball. The side nearest the 
sealing w T ax becomes positively charged, and the farther side 
becomes negatively charged. 

Since bodies with unlike kinds of electrification attract, 
and those with like kinds repel, the pith ball is both at- 
tracted and repelled ; but the law of inverse squares, as 





STATIC ELECTRICITY 227 

stated in section 229, holds for electricity as well as mag- 
netism. Because of the difference in distance, the attrac- 
tion is greater than the repulsion, and the pith ball moves 
toward the sealing wax. As the distance between them grows 
less, the difference between attraction and repulsion grows 
rapidly greater. When the space between the sealing wax 
and the pith ball is about equal to the diameter of the ball, 
the attraction will be four times as great as the repulsion. 
When the distance becomes one quarter as great, the attrac- 
tion will be sixteen times as great as the 
repulsion, etc. Thus the pith ball moves 
faster and faster as it approaches the elec- 
trified body. When it touches, there is a 
flow of electricity from the neutral body 
to the other, until they are in the same 
state. Then repulsion begins and the pith 
ball flies off from the sealing wax. It 
is now negatively charged, and will act 
toward a neutral object as the sealing wax acted toward it. 
If it is brought near to a neutral body it polarizes it, so 
that attraction is greater than repulsion between them. If 
the neutral body is heavier, or is not free to move, the pith 
ball will move to it. If the neutral object should be a 
second pith ball, of equal weight with itself (Fig. 132), they 
will move equal distances toward one another. When they 
touch there will be a flow of electricity from one to the 
other, and they will then be exactly alike, and repel. The 
second ball will produce exactly the same effect toward 
neutralizing the first ball as the first does toward electrify- 
ing the second. Hence, every time an electrified conductor 
charges another body, it tends to neutralize itself. This is 
different from magnetism. A magnet is not at all weak- 
ened by magnetizing other pieces of iron. In the next two 
sections we shall see how an electrified body may enable us 
to electrify any number of other bodies, without itself be- 
coming discharged at all. 



228 PHYSICS 

236. By Induction a Polarized Body may receive a Charge 
from a Neutral Body. — Fig. 133 represents an electrified stick 
of sealing wax held near to a neutral pith ball, so as to influ- 
ence it without contact. The pith ball is polarized and 
drawn toward the sealing wax, as explained in section 235. 
If now the sealing wax shquld be removed, the pith ball 
would return to its former neutral state ; but if, while it is 
polarized under the influence of the sealing wax, a neutral 
object, as for example one's finger, is allowed to touch the 
pith ball and after that the sealing wax is removed, the pith 
ball will be found to be positively charged. While we must 

guard against thinking that we know 
just what happens, it is interesting to 
learn what those who have thought much 
about these things have conjectured. 
Benjamin Franklin conjectured that it 
might be something like this : The elec- 
tricity of the pith ball may have accumu- 
lated, under the influence of the sealing 

wax, in the under part of the ball, leav- 
FiG. 133. ' r . 

ing the upper part rather destitute. This 

fact he indicated by the -j- an( i — signs. When another 

object touches the pith ball, electricity flows in to fill the 

vacancy, and now when the sealing wax is removed the ball 

has more 'than the normal charge. 

237. The Electrophorus. — This is a further illustration of 
the subject presented in the last section. A jelly-cake tin 
with sealing wax melted in it, and hardened into a layer 
from an eighth to a quarter of an inch in thickness, makes 
a satisfactory form of electrophorus. It serves as a con- 
venient means for electrifying other objects, without losing 
its own charge. The sealing wax is rubbed with flannel. 
This, by induction, enables us to electrify a neutral disk, 
from neutral objects, an indefinite number of times. An- 
other jelly-cake tin, a little smaller in size,- serves well for 
the neutral disk. This disk when charged is handled by 



STATIC ELECTRICITY 229 

means of silk threads for insulation (see Fig. 134). The 
sealing wax, being a non-conductor, does not impart elec- 
tricity to the neutral disk in sufficient quantities to charge 
it, as a stick of sealing wax may charge a pith ball. In- 
deed, the points of contact between the sheet of wax and 

the neutral disk are extremely 
slight. The result is that the 
metal disk is polarized while 







+ 



Fig. 134. Fig. 135. 

resting upon the wax, as shown in Fig. 135, where a b rep- 
resents the metal disk and c d the sealing wax. If now one 
touches the disk with his finger, while in this condition, 
the disk becomes positively charged in the same manner 
as the pith ball described in section 236. If the disk is 
lifted by the silk threads, it will carry away a positive 
charge as many times greater than that which a pith ball 
would carry as its area is greater than that of the pith 
ball. The process may be repeated an indefinite number 
of times without again rubbing the wax with the flannel. 
The disk is charged each time by electricity from the earth 
flowing through the body of the operator and off the finger 
with which he touches the disk. If this charged disk is 
brought near to any neutral object, the discharge is marked 
by a spark of considerable length. This spark will light 
the gas if the disk is presented to a gas jet. It will ex- 
plode the mixture of oxygen and hydrogen in the eudi- 
ometer (see Fig. 1, page 9). If one brings a finger to this 
charged disk after it is removed from the influence of the 
sealing wax, which, as we say, holds the charge " bound," 
he will experience, when the spark passes, a slight prick- 
ing sensation. We may, however, store, so to speak, several 



230 



PHYSICS 




Fig. 136.— Electrophorus. 



of its charges in a condenser, described in the next section, 
so that one will feel a larger shock, when the charge is 

taken all at once, through the 
body. 

A very common form of 
electrophorus is shown in Fig. 
136, which consists of a cake 
of hard rubber and a metal 
disk with a glass or hard-rub- 
ber handle. 

The electrical machines in 
common use (see Fig. 137) 
work upon the same principle 
as the electrophorus. Kotat- 
ing the glass disk accomplishes precisely the same thing as 
carrying a charge by means of the metal disk of the elec- 
trophorus and delivering it to some object. The machine 
delivers a continuous flow of charge through a conductor. 
These machines also have 
attached to them con- 
densers, described in the 
next section. 

238. Condensers. — A 
large beaker of chemical 
glassware makes a good 
condenser. The inside 
and outside are gilded, or 
covered with tinfoil, to 
about two inches from 
the top. Suppose this is 
held upon the hand, as 
shown in Fig. 138, and the electrified cover of the electro- 
phorus is brought to the outer coating. The outer coating 
becomes positively electrified, and this polarizes the inner 
coating by induction. The positive electrification is dis- 
charged through the hand, leaving the inner coating nega- 




Fig. 137. — Electrical machine. 



STATIC ELECTRICITY 



231 



ill 

ill! 



Fig. 138. 



tively electrified. If now the other hand is brought to the 
outer coating, the coatings of the beaker neutralize each 
other by discharging through the body. If 
the cover of the electrophorus is discharged 
into the outer coating of the beaker several 
times, we find the shock produced by the 
discharge proportionally increased. Twenty 
sparks from the electrophorus will charge 
the condenser sufficiently to send a consid- 
erable shock through a class of thirty or 
forty pupils with hands joined. Condensers 
have a variety of shapes. The most con- 
venient form is that of the Ley den jar, illus- 
trated in Fig. 139. The name is derived 
from the city of Leyden in Holland, where it was invented 
in the year 1746. 

239. Lightning. — The earth, the air, and the clouds con- 
stitute a natural condenser like a huge Leyden jar. The 

clouds constitute 
one coating, the 
earth the other, and 
the atmosphere rep- 
resents the glass in- 
sulator between the 
two. This natural 
condenser becomes 
charged in various 
ways. Evaporation 
is perhaps one cause 
of electrification. 
If the vapor is posi- 
tively charged, as it 
accumulates in the 
clouds, it induces a 
negative charge in objects upon the earth's surface, im- 
mediately underneath the clouds. Lightning is the spark 




Fig. 139. 



232 



PHYSICS 



which attends the discharge of this natural condenser. It 
frequently happens that the vapor of one cloud is positively 
charged with reference to that of another, and it is prob- 
able that the lightning discharge between two clouds is of 
much more frequent occurrence than that between cloud 
and earth. 

240. Electrical Distribution— Effect of Points.— If the 
electrified body is a non-conductor, the electrification ap- 
pears only in those spots where it was produced ; but if the 
body is a conductor, the charge spreads itself over all the 
surface. The opposite extremities are not poles, as in the 
case of a magnet, nor is the intervening part neutral. The 
charge, however, whether positive or negative, affects the 
outer surface only, and this gives us trouble with Franklin's 

conjecture, men- 
tioned in section 
236. The fact is, 
that if the gild- 
ing of an electri- 
fied pith ball should fall 
off, it would remove all 
signs of electrification, 
whether -f- or — , from the 
pith ball. This is shown 
by an experiment with the 
apparatus illustrated in 
Fig. 140. A neutral ball 
upon an insulated sup- 
port is covered with two 
metal hemispheres. It is 
electrified either before or after the hemispheres are put 
on; but when the hemispheres are removed by the glass 
handles they alone are found to be electrified. The sphere 
itself is left in a neutral state. If an insulated tin cup is 
electrified, no sign of a charge will be found inside the cup, 
but only upon the outer surface. The charge is also found 




STATIC ELECTRICITY 



233 





Fig. 141. 



to be most intense upon projecting portions, as the handle 
of the cup. If an egg is insulated and electrified the 

greatest in- 
tensity of 
charge will be 
found upon 
the small end 
of the egg. 
If we con- 
struct an object egg-shaped, 
but with the small end very 
much drawn out, as in Fig. 
141, the difference between 
the intensity of the charge 
upon this prolongation and 
the rest of the surface will 
be very marked. If the small end is made into a sharp 
point, the tension of the charge will be increased at this 
point to such an ex- 
tent that the elec- 
tricity which, as 
was said in section 
234, always leaks 
away to some ex- 
tent, will disappear 
rapidly. Hence, 
objects like the 
pith ball, which 
should retain a 
charge, are made as 
round and smooth 
as possible. This 
accounts for the 
many knobs upon 
electrical apparatus. When points are used, as, for example, 
the "combs" on the electrical machine (see Fig. 137), they 




Fig. 142. 



234 



PHYSICS 




are to facilitate the discharge from one portion to another 
of the apparatus. If a portion of the electrical machine 
has a point projecting from it, as shown in Fig. 142, it 
will create a sufficient breeze to blow out a candle. This 
may be accounted for by supposing that the particles of 
air are electrified and thrown off at this point, like pith 
balls, in a stream. If the points are 
arranged at the extremities of the 
spokes of a wheel, as shown in Fig. 
143, the wheel will rotate as a lawn 
sprinkler, which throws off streams 
of water from its arms. As has been 
already stated, an electrified cloud 
induces the opposite state of electri- 
fication in that portion of the earth 
which is immediately underneath it. 
Mountain peaks, spires of buildings, 
lightning rods, masts of ships, etc., 
like points upon electrical appara- 
tus, facilitate the discharge between 
the earth and the clouds. If an electrical machine is oper- 
ated in a dark room, a pale light is seen to stream from 
sharp points upon the machine. This phenomenon occurs 
in Nature on a grand scale. Sailors notice pale flames 
streaming from the tips of the masts when a strongly elec- 
trified cloud is passing over. This is called by them St. 
Elmo's Fire. 




Fig. 143. 



CHAPTEE XXV 



ELECTRIC CURRENTS 



I. GENERATORS OF ELECTRIC CURRENTS 



241. Sources of Electric Currents. — Observe that we do 
not say sources of electricity. That would be inconsistent. 
Assuming electricity to be identical with the ether, we can 
neither create nor destroy it. But electricity may be set in 
motion ; this flow of electricity from one point to another 
is the subject of this chapter, and we may properly begin 
with the sources of the 
current. The discharge 
of a Ley den jar, or other 
electrified body, through 
a conductor, is a current 
of electricity. If we con- 
nect the two knobs of the 
electrical machine repre- 
sented in Fig. 144 by a 
copper wire, a constant 
current of ' electricity 
flows through the wire 
while the machine is 
operated. The current produced by this machine is, how- 
ever, extremely slight in quantity, and is therefore of little 
use, although, as was stated in section 234, it has exceed- 
ingly high tension and can push its way through poor con- 
ductors. A few analogies will help to make clear the dis- 
tinction between high-tension and large-quantity currents. 

235 




Fig. 144. — Electrical machine. 



236 PHYSICS 

The current which we get from the electrical machine men- 
tioned above may be compared with a stream of water com- 
ing through a pin hole in the bottom of a very deep tank 
which is full of water. Although the " head of water " may 
be very great, the quantity is too small to turn a mill 
wheel. Or it may be compared with a pile driver weighing 
only one ounce, but raised to a great height. It falls with 
great velocity, but with too little momentum to move the 
pile. Or it may be compared with a cup of water heated to 
the boiling point. Its temperature is very high, but the 
quantity of heat is too small to modify the climate, or to 
heat a house or to cook a dinner. In these analogies water 
pressure, velocity, and temperature represent electric tension. 
In the present chapter we shall discover means for produ- 
cing electric currents in larger quantities, although the 
tension will be quite low and they will not flow through 
much resistance. By way of analogy they may be compared 
with the flow of a large stream of water, having only a few 
feet of fall but capable of operating a water wheel. Or 
they may be compared with a pile driver of considerable 
size, capable of driving a pile by falling only a few feet. 
Or they may be compared with a large body of water 
slightly warm, but able to modify the temperature of sur- 
rounding objects for a long time by reason of its large 
quantity of heat. 

We shall present in this chapter three sources of cur- 
rent — chemical action, mechanical motion, and heat — and 
these forms of energy are transformed into current by 
means of the battery, the dynamo, and the thermopile re- 
spectively. Turning back for a moment to the general 
conception of work, it will be recalled that work is the 
overcoming of resistance through space, and involves both 
motion and something to be moved. Energy, or the power 
to do work, is only possible, therefore, when we have mat- 
ter in such a position that it is capable of motion. This 
means inequality of condition, and therefore possible ex- 



ELECTRIC CURRENTS 237 

change. The weight on top of the pile .driver represents 
stored-up work simply because there is a lower level to 
which the weight may fall. The steam in the boiler repre- 
sents stored-up work simply because there is a lower tem- 
perature to which the steam may fall. All matter at the 
same level, all bodies at the same temperature, represent no 
possible interchange, and therefore no available energy. 
Lift some of the matter above the general level, and at 
once we have potential energy. Heat some of the bodies 
above the general temperature, and we have available en- 
ergy. The water upstream turns the mill because of the 
lower level downstream. Applying this thought to elec- 
tricity, we see that so long as the electric level is undis- 
turbed, there is no electric current. The universe is as 
full of electricity as the ocean is of water, but just as the 
ocean must be lifted up by evaporation and precipitated in 
rain upon the hills before it is available as a water power, 
so to make electricity available as a source of energy we 
must disturb its level, and we must provide a suitable chan- 
nel through which the equilibrium may be brought about. 
All devices for producing electric currents may be regarded 
as devices for changing the electric level, and all conduct- 
ors as channels for bringing about equalization of level. 
If the difference of level is temporary, the current will be 
temporary ; but if the difference of level is constantly 
maintained, and the channel remains the same, the current 
will also be constant. 

242. Electric Potential is the term applied to electric 
level. Currents flow from a place of high potential to a 
place of low potential. In case the potential is equal, 
there is no flow of current. The production of current is 
practically the process of maintaining a difference of po- 
tential. This is also called electro-motive force, abbreviated 
to E. M. F., or simply E ; the unit for the measurement of 
which is called the volt (254), a name derived from Volta, 
the inventor of the voltaic cell. 




238 PHYSICS 

243. The Voltaic Cell (Fig. 145) is a machine for main- 
taining a constant difference of potential through constant 
chemical action. In its simplest form it consists of two 
metals joined by a conductor and moistened by some liquid 
that will dissolve one of them. A jar of water acidulated 

with sulphuric acid, H 2 S0 4 , 
and containing a strip of cop- 
per and a strip of zinc, con- 
stitutes a simple voltaic cell. 
On joining the copper and the 
zinc by a wire, a current flows 
from the one to the other. 
Meanwhile the zinc is being 
acted upon by the acid, and is 
passing into solution as zinc 
sulphate, ZnS0 4 , while bubbles 
Fig. 145.-The voltaic cell. of hydrogen, H, appear on the 

copper plate. The chemical 
action is as follows : Zn + H 2 S0 4 = ZnS0 4 + 2H. The 
source of current here is the chemical action between the 
zinc and the acid. The copper remains unchanged, but 
in its absence we should have no current ; we should have 
the same chemical reaction, but the physical product would 
be heat. The solution would become very hot. The cop- 
per largely prevents this production of heat, and causes the 
energy to appear as electric current. The zinc, being the 
metal acted upon, and the apparent source of the differ- 
ence of potential, is termed the electro-positive metal, while 
the copper is the electro-negative metal. 
The galvanic cell consists, then, of — 

1. The electro-positive metal. 

2. The electrolyte, or substance which will produce a 
chemical reaction with the positive metal. 

3. The electro-negative element. 

We may substitute for zinc any other metal that will be 
acted upon by the electrolyte chosen. Instead of the sul- 



ELECTRIC CURRENTS 239 

phuric acid, we may use any other substance that will 
produce a chemical change with the electro-positive metal. 
And, finally, the electro-negative element may be any con- 
ductor, such as platinum or carbon — that is, insoluble or 
less soluble than the electro-positive metal. It need not 
itself be a metal. 

By means of a condensing electroscope, the upper end 
of the carbon can be shown to be positively but very feebly 
charged, and the upper end of the zinc to be likewise nega- 
tively charged by a conductor, wire or other. In order that 
there may be a current of electricity, there must be a com- 
plete circuit — that is, the upper ends of the carbon and the 
zinc mast be connected. We think that the current flows 
through the wire from the carbon to the zinc, and through 
the solution from the zinc to the carbon. 

For convenience in introducing various pieces of appa- 
ratus into the electric circuit we have two wires, one con- 
nected with the carbon and the other connected with the 
zinc. The free ends of these wires are called poles. The 
free end of that connected with the carbon is called the 
positive pole, and the free end of the other wire is called 
the negative pole. In short, any point in the circuit is 
positive with reference to any other point in the circuit 
toward which the current flows, and negative with refer- 
ence to any other point in the circuit from which the cur- 
rent flows. So that in the solution the zinc is positive 
with reference to the copper or carbon ; but outside of the 
cell the wire connected with the copper or carbon is called 
the positive pole or the anode, while that connected with 
the zinc is called the negative pole or kathode. 

244. The Electro-Chemical Series. — Since we need only 
chemical action and a suitable conductor, the choice of ma- 
terials for a galvanic cell covers a wide range. But what we 
are working for is a strong, constant current of electricity, 
and so our choice of material must practically be limited to 
combinations that will give this result. If we arrange the 



240 PHYSICS 

available chemical elements in a list according to their 
properties, putting those first which are the most readily 
oxidized, we shall find that the strongest current results 
when two widely separated elements are chosen. Such a 
list would stand as follows : 

+ Sodium. Copper. . 

Magnesium. Silver. 

Zin c. Gold. 

Lead - Platinum. 

Tin - -Carbon. 
Iron. 

The alkali metals, such as sodium, and the alkaline-earth 
metals, such as magnesium, are practically ruled out on 
account of the too great energy of their chemical affinity 
and their expense. Zinc, therefore, is the electro-positive 
metal usually chosen. At the other end of the series cop- 
per and carbon are the electro-negative elements most 
frequently used. But any element in the list is electro- 
positive with respect to the element following it, and elec- 
tro-negative to the one before it. The order of the list 
also represents the heat-producing power of the elements. 
This is very significant when we remember that the chem- 
ical action yields heat when the conditions are such that it 
may not yield a current, as when the copper or carbon is 
wanting. 

245. Local Action and Polarization. — The zinc-carbon- 
sulphuric acid cell just described is not a very practical 
machine, for two reasons : the zinc wastes away when the 
cell is not in operation, and the current is far from con- 
stant. The waste is due to local action, and the uncon- 
stancy to polarization. 

Local Action. — If chemically pure zinc be used, it will 
only dissolve when it is in connection with the carbon and 
the current is flowing. But the zinc of commerce is far 
from pure. It contains appreciable quantities of iron and 
carbon, and dissolves in the acid even when not connected 



ELECTRIC CURRENTS 241 

with the copper. This is due to local action between the 
zinc and the iron or other impurity by which we have 
internal currents set up, and, as a result, constant waste. 
It may be avoided by amalgamating the zinc. A few drops 
of mercury are rubbed over the clean and acid-moistened 
plate of zinc, forming a surface amalgam. The impurities 
do not dissolve in the mercury. Hence the plate acts like 
pure zinc, and the amalgam goes on forming during the 
action of the cell, just as rapidly as the zinc is dissolved 
out by the acid. 

Polarization is a more serious evil. The hydrogen lib- 
erated by the chemical action of the zinc and sulphuric 
acid is electro-positive, and hence gathers upon the carbon 
or electro-negative plate. This not only acts as an insu- 
lator of the negative plate from the current — the gas not 
being so good a conductor as the solution — but it lessens 
the difference of potential between the two plates. Indeed, 
the hydrogen, if it should completely cover the carbon 
plate, would change it from an electro-negative to an elec- 
tro-positive plate. The current in consequence grows 
weaker and weaker, the carbon plate is said to be polar- 
ized, and can only be restored to full action by the removal 
of the hydrogen. Different methods have been suggested 
for the prevention of polarization, and have given rise to 
our present large number of kinds of voltaic cells, some of 
which are mentioned in the following list : 

246. Some Typical Cells. 

E. M. F. 
Volts. 

Bichromate cell 2.1 

Bunsen cell 1.9 

Leclanche cell 1.4 

Daniell cell 1.05 

Gravity cell 1.05 

In the bichromate cell (Fig. 146) the zinc plate is sus- 
pended between two plates of carbon, and, being attached 
to an adjustable rod, may be drawn up into the neck of the 
17 



242 



PHYSICS 



^*% 




bottle and quite out of the solution when the cell is not in 
use. Chemical depolarization depends in all cases upon 

the action of an oxidizing agent. 
The hydrogen is thus changed 
into water, H 2 0. In the bichro- 
mate cell the oxidizing agent is 
bichromate of sodium, Na 2 Cr 2 7 . 
About one pound is added to a 
gallon of water and a pint of sul- 
phuric acid. When the solu- 
tion is fresh it is bright red, but 
gradually turns dark and green 
from the reduction of the bi- 
chromate. The capacity of the 
jars varies from half a pint up to 
a gallon. The bichromate cell 
has long been a favorite one for 
lecture use, as it gives a powerful 
current and is always ready. 
The Bunsen cell (Fig. 147) is a double-fluid cell. The 
electro-negative element is carbon, immersed in the oxidiz- 
ing agent, strong nitric acid, HX0 3 , contained in an inner 
porous cup. The zinc is 
amalgamated, and is in the 
form of a cylinder open at 
both ends. It surrounds the 
porous cup, and stands itself 
in dilute sulphuric acid. The 
hydrogen liberated by the solu- 
tion of the zinc passes through 
the porous cup, but fails to 
reach the carbon, because it 
meets the nitric acid and is 
oxidized to II 2 with the lib- 
eration of red fumes of nitro- 
gen peroxide, N0 2 . The cell Fig. 147.— The Bunsen cell. 



Fig. 146.— The bichromate cell. 




ELECTRIC CURRENTS 



243 



is strong and constant, but the peroxide fumes are corro- 
sive and poisonous. 

The Leclanche cell (Fig. 148) is a single-fluid combina- 
tion in which zinc and carbon are immersed in a solution 
of ammonium chloride, NH 4 C1, and polarization is pre- 
vented by surrounding the carbon with a packing of mixed 
carbon and black oxide of manganese, Mn0 2 . The zinc 
may be in the form of a pencil, or a cylinder surrounding 
the carbon. The action is very simple. The zinc forms a 
soluble double chloride of zinc and ammonia, while free 
hydrogen and ammonia gas, NH 3 , pass toward the carbon. 
But the oxide interposes, tak- 
ing care of the hydrogen, and 
the ammonia gas escapes in- 
to the air. The oxide of man- 
ganese is itself reduced to a 
lower oxide, and must in time 
be removed. These cells are 
used in almost every house 
for ringing electric bells. 
Their great virtue is that no 
chemical action takes place 
in them except when the 
electric current is flowing. 
Hence they are known as 
" open - circuit " batteries. 
For ordinary household pur- 
poses they may last a year or 
two without any replenishing 
of parts. 

Tlie Daniell cell introduces an entirely new method of 
preventing polarization. A copper plate is immersed in a 
solution of copper sulphate, CuS0 4 , in the outer glass jar, 
and zinc is immersed in sulphuric acid in an inner porous 
jar. The hydrogen which is set free by the action of the 
sulphuric acid upon the zinc passes through the porous cup, 




Fig. 148.— The Leclanche cell. 



244 PHYSICS 

but instead of collecting upon the copper plate it decom- 
poses the copper sulphate, forming H 2 S0 4 and setting the 
copper free which is deposited upon the copper plate. The 
copper, being electro-negatiye, does not change the char- 
acter of the negative element, and the current therefore is 
almost constant. The outer liquid is maintained a satu- 
rated solution of copper sulphate by crystals of the salt. 

The gravity cell (Fig. 149) is a modification of Daniell's, 
and dispenses with the porous cup. The copper rests on 
the bottom of the jar. A saturated solution of copper sul- 
phate completely covers the copper, extra crystals of the 
sulphate being placed in the bottom. The zinc is sus- 
pended from the top of the jar, about four inches above the 
z copper. It is surrounded by a solu- 
+ A j - tion of zinc sulphate, which, being 

|iK||^Hi|yH l ess dense, floats on top of the heavy 

JSPiHifH copper sulphate solution. The cell 

ZnS ° 4 K gets its name fr ° m the fact that 

|j jliL _ 2 i gravity replaces the porous cup in 

CwS04 |£J~_ - 111 keeping the two solutions apart. 

j,U' ;r?.f ,J| _^m The zinc sulphate increases as the 

^|8||~ \ ■•'" $00^~ z i llc wastes away, and must be re- 

Fig. 149.-The gravity cell. m0ved fr0m time to time « Tne 

copper sulphate is used up, and 
must be renewed by dropping fresh crystals into the bot- 
tom of the jar. As the copper sulphate forms a deep-blue 
solution, one can always tell when more crystals are needed. 
The blue color should extend above the copper, but never 
quite reach the zinc. 

On account of its convenience, economy, and constancy, 
the gravity cell is used almost entirely for telegraphic 
work. One may see them at nearly every railway station. 

The number of actual and possible cells is legion. We 
have described only those which are to-day most important 
and most frequently met. They are all simple machines 
for maintaining a more or less constant difference of poten- 



ELECTRIC CURRENTS 



245 



tial between two points, and consequently setting up an 
electric current. 

247. The Battery of Cells. — When several cells are joined 
together, they form a voltaic battery. If the positive 
metal of one cell is joined to the negative element of the 
next cell, and so on throughout the series, 
the current passes through one cell after an- 
other, and the battery is said to be arranged 
in series (Fig. 150). Thus the difference in 
the potential of carbon and zinc 
of each cell is multiplied by the . 





Fig. 150.— Cells in series. 



Fig. 151. — Pumps in series. 



number of cells, and a battery of three cells so arranged 
will push its current through three times as much resist- 
ance as one cell would be able to do. The analogy of 
three water pumps, arranged as represented in Fig. 151, 
will help to make this clear. All the water which traverses 
the circuit must go through each pump. Each pump 
raises the water level by a certain amount, and it is mani- 
fest that the water pressure in the return pipe is three 
times as great as it would be if it returned from the outlet 
of the first pump. 

If all the positive metals are joined together and all the 
negative elements, the current passing through all the cells 
at the same moment, the battery is said to be arranged in 
parallel (Fig. 152). This is analogous to the arrangement 
of pumps represented in Fig. 153, where only one third of 
the water goes through each pump. Three pumps raise 



246 



PHYSICS 



the level of the water no higher than one pump would, and 
the water pressure in the return pipe is no greater than it 
would be if one pump acted alone, but three times as great 



z c z c z c 




Fig. 152.— Cells in parallel. 



Fig. 153. — Pumps in parallel. 



a quantity of water may be supplied to the return pipe as 
in the former case. The arrangement chosen must depend 
upon the work to be done, and this will be discussed in 
section 257. 

II. Some Effects of Electric Currents 

248. Electric Currents recognized by their Effects. — To a 

casual observer there is no evidence that the cell produces 
an electric current, and we must therefore learn to recog- 
nize the current from some effect which it may produce. 
We will stop to study some of the effects of the current 
before we go on to consider its further production by the 
dynamo and thermopile. These effects cover a very wide 
range, and the immense variety of the phenomena growing 
out of electricity constitutes its chief fascination. Those 
which we shall consider are physiological, thermal, chemical, 
and magnetic. 

249. Physiological Effects.— It is difficult to get any evi- 
dence from our sense of feeling that the cell produces any 
electric current, because our bodies are not sufficiently 
good conductors (see 234) for the cell, with its slight poten- 
tial, to send any of the current through our flesh. Of 
course, a sufficiently large number of cells arranged in series 



ELECTRIC CURRENTS 247 

would send a current that might be felt, but the batteries 
of such number of cells as we are likely to use in the lab- 
oratory are not capable of sending through the human body 
any appreciable current. If the poles of two or three cells 
connected in series are touched to the tip of the tongue a 
few millimetres apart, a slight sensation is felt, but the 
amount of current that passes is exceedingly small. We 
may therefore handle our battery wires without insulation 
and lose no current. For more interesting physiological 
effects we must have high-tension currents, such as will be 
considered in future sections upon induction. 

250. Thermal Effects. — Whenever a current meets resist- 
ance, heat is produced in much the same way as when me- 
chanical motion encounters friction. In both cases there 
is waste of energy. Even the best conductors offer some 
resistance, and consequently the temperature of every con- 
ductor rises a little while an electric current is passing 
through it. In the case of all forms of electric light we 
purposely introduce resistance to the current, so as to get 
heat and light from it. In the arc lamp the tremendous 
resistance of the air produces the voltaic arc, one of our 
most intense sources of heat. In the incandescent lamp 
the high resistance of the filament of carbon develops 
enough heat to make the carbon white hot. 

Electric stoves are simply resistance boxes. The elec- 
tric stove used in the trolley cars consists of several coils of 
wire. They offer so much resistance to the passage of the 
current that they become much heated, and then act simply 
as radiators. In the stoves used for cooking the wires are 
generally of platinum or German silver, buried in fire clay 
or in asbestos. 

The electric furnaces used to reduce ores of aluminium 
and other metals consist of a fire-clay box provided at each 
end with a carbon terminal, and packed with a mixture of 
carbon and ore. When the current passes it meets such 
tremendous resistance that a corresponding .amount of 



248 PHYSICS 

heat is developed, and the refractory ore is reduced to 
metal. 

The current is applied with great success to the welding 
of metals. The pieces to be welded are pressed together 
with much force, and a large current is passed through the 
juncture. Great heat is developed and the welding is very 
perfect. 

The solutions in the battery cells rise in temperature 
when the current passes, because of the resistance which 
they offer to the current. 

If the wires from a battery of two cells connected in 
series be rubbed upon a file, a brilliant shower of sparks 
will be produced. Minute particles of metal are made in- 
candescent by the resistance offered to the current as the 
wires dance along over the file. 

251. Chemical Effects. — The chemical action in the cell 
produces an electric current, and this electric current is in 
turn able to produce chemical action. In the cell zinc de- 
composes the sulphuric acid, forming zinc sulphate, which 
remains dissolved in the water used in the cell. If, when 
the cell is " run down," we dip the poles of a sufficiently 
strong battery into this solution of zinc sulphate, the elec- 
tric current will decompose this zinc sulphate again, the 
zinc gathering about the negative pole and the sulphuric 
acid gathering about the positive pole. This process of 
decomposing compounds by electricity is called electrolysis. 
When we have decomposed this zinc sulphate into zinc and 
sulphuric acid it will act as a battery cell and produce 
again an electric current. This is one form of a storage 
battery, and the act of decomposing its zinc sulphate into 
zinc and sulphuric acid by means of an electric current is 
called storing the battery cell, or storing electricity — an 
expression which is misleading. 

Storage batteries, or accumulators, were first announced 
in practical form by Gaston Plant e in 1860. In its com- 
monest form the storage-battery cell consists of two plates 



ELECTRIC CURRENTS 249 

of lead, each having holes filled with a paste of lead sul- 
phate, in dilute sulphuric acid. When an electric current 
is passed through this cell the anode (the plate of lead 
which is the positive pole — that is, which is connected with 
the wire from the negative plate in the battery) becomes 
covered with a coating of peroxide of lead, Pb0 2 , while the 
kathode is covered with particles of lead in a spongy form. 
In this condition the accumulator is said to be " charged." 
For this reason it is sometimes called a storage battery, but 
in reality electricity is not stored in it any more than heat 
is stored in coal, or houses and farms are stored in a bank. 
The electric current sent through the accumulator does 
chemical work in breaking chemical compounds, which, 
when they reform again, will generate a current. It is a 
curious fact that these chemical compounds do not reform 
again in the cell until the circuit is closed and the electric 
current produced thereby flows. Yet this is the case with 
every battery cell to a certain extent, and particularly so 
with those, such as the Leclanche type, which are called 
" open-circuit " cells. Storage batteries are much used for 
running electric launches and automobiles, and to supple- 
ment a dynamo, from which it may store energy to be 
expended at intervals when the dynamo is insufficient or 
at rest. 

Electrolysis of Water. — This is conveniently carried out 
in the Hoffmann apparatus, shown in Fig. 154, or some 
other simple form like that represented in Fig. 155. The 
water has a little sulphuric acid added to it, in order to 
make it a conductor of electricity. The current from a 
battery of several cells is allowed to pass through the appa- 
ratus until enough gas has been collected in each tube to 
be examined satisfactorily. Twice as much gas collects at 
the negative electrode (the kathode) as at the positive elec- 
trode (the anode). The first-mentioned gas is found to 
burn with a pale-blue flame ; it is hydrogen. The gas at 
the anode, when tested by a glowing splinter, is shown to 



250 



PHYSICS 



be oxygen. The decomposition is expressed by the chem- 
ical reaction 

H 2 = H 2 + 0. 

Electrolysis of Salts. — The current may be used to de- 
compose water solutions of any of the salts of the more 
electro-negative metals, such as copper, nickel, silver, and 

gold. This is the basis 
of our electroplating and 
electrotyping. The object 
to be plated is made the 
kathode, the anode being 
either a plate of the metal, 
in which case the solution 
or " bath " keeps a con- 
stant strength, or else a 
strip of platinum (Fig. 
156). The cyanides of gold 
and silver are generally 








- 


\o\ 


H 






1 i 
jj§ 




wiiiijllliyp 


-.-- ; ; ~ 


"";'"".-■'" 


1b 


. 



""''^''"iiiiiiiiiliillllllllllllllllilill 

Fig. 154. — Hoffmann apparatus. 



Fig. 155.— Electrolysis of water. 



employed, and a double sulphate of nickel and ammonia. 
Copper succeeds best from a slightly acid solution of the 
sulphate. In electrotyping, an impression of the type or 
cut is first made in wax or gutta-percha, and this is then 
rubbed over with graphite, in order to make it a conductor. 



ELECTRIC QUERENTS 251 

The mold is then suspended in a bath of copper sulphate 
as a kathode, the anode being a copper plate. In this way 
a very thin film or skin of copper is obtained, which is 




Fig. 156. — Electroplating. 

afterward backed with type metal and mounted on a 
wooden block, so as to make its face height equal to that 
of ordinary type. 

Most of the copper ore of the world is bought and sold 
on the basis of the " electrolytic assay." About a gram of 
ore is digested with acid. The insoluble " gang " is filtered 
off. The dissolved copper is placed in a weighed platinum 
dish, which is then made the kathode, a little spiral of 
platinum dipping into the solution being the anode. The 
current is allowed to pass overnight. In the morning all 
the copper is found deposited on the platinum dish, and, 
after drying, may be directly weighed. 

252. Magnetic Effects. — If the copper wire which con- 
nects the carbon and zinc terminals of a cell is made into 
a coil as shown in Fig. 157 — which coil is called a helix — 
the electric current will develop a magnetic field. The 
region around this helix behaves exactly as that around 
all magnets. 

We regard a magnetic field as an ether vortex, and to 
produce this we cause the electric or ether current to move 
in whirls. The successive turns of the wire must not touch 



252 



PHYSICS 



one another, for if they did the current would take the 
shortest path from the carbon to the zinc. The best way 
to make the helix is to nse wire which has a thin insulating 
covering. No. 24 single, cotton-covered copper wire is 






Fig. 157.— Helix. 



Fig. 158. 



best. This may be coiled around a wire nail, making a 
helix about an inch long, with the wires, say, three layers 
deep. The nail may then be withdrawn, and the helix, 
when an electric current is passing around it, will be found 
to be the center of a rather strong magnetic field. The 




Fig. 159.— The floating helix. 

end of this helix, around which the current is passing in 
the direction in which the hands of a watch move, will be 
found to attract the north pole of a compass needle — that 
is, it is a south pole, and the other end of the helix is its 



ELECTRIC CURRENTS 253 

north pole (see Fig. 158). Such a helix may be floated 
upon a battery solution, and will itself behave as a compass 
needle (see Fig. 159). If the wire nail is inserted in this 
helix it will be strongly magnetized when the current 
passes, and the field will be found to be much more strongly 




m& 



Fig. 160. 

magnetic than before the iron core was used. A helix with 
an iron core is called an electro-magnet. We shall meet 
with it many times in future sections. If the iron is very 
soft, it will lose its magnetism as soon as the current ceases 
to flow. If, however, it is steel or hardened iron, it will 
retain its magnetism after it is removed from the helix. 
In this way we may make permanent magnets of steel 
(Fig. 160). 

We are now prepared to state what we believe to be the 
connection between magnetism, static electricity, and elec- 
tric currents. Magnetism we regard as an ether vortex, 
static electricity is an ether stress, and an electric current is 
ether flowing in a stream. The ether vortex is not confined 
to the magnet, although that is its center ; the vortex ex- 
tends some distance around the magnet, and is called the 
magnetic field. Ether stress is not confined to an elec- 
trified body, although that is the center of it. By bring- 
ing a pith ball near to an electrified body, we discover 
that the ether stress extends to some distance around the 
body. 

An ether current is not confined to the conducting 
wire, although that is the center of the stream. We shall 
learn more about this in future sections. 



254 



PHYSICS 



If we bring a magnetic needle near to a straight wire 
through which a current is passing (Fig. 161), we have evi- 
dence that the field about the wire is affected by the elec- 




^MM 



trie current. The needle will be deflected toward a direc- 
tion at right angles to the wire. The accompanying 
diagrams (Fig. 162) show the direction which the needle 
will take, and at the same time suggest the explanation. 
Suppose the current to be flowing from left to right, as 
represented by the large straight arrow in the upper dia- 
gram, and the needle to be brought over it, the north pole 
is turned toward the observer ; if under it, the south pole 



a 



H 




Fig. 162. 



Fig. 163. 



is turned toward the observer. This permits the ether 
whirl to move with the ether flow. If the current flows 
from right to left, as represented by the large straight arrow 



ELECTRIC CURRENTS 



255 



in the lower diagram, the needle will be deflected as there 
represented. 

The galvanometer, for which we shall have much use in 
future sections, is presented here as an illustration of 
magnetism in a helix, a b (Fig. 163) is a coil of wire about 
six inches in diameter. Suspended in the center of this 
coil or helix is a small magnetic needle. If the electric 
current is sent around the coil in the direction of the 
arrow, a magnetic field will be created, the south pole of 
which is on the side of the helix toward the observer, and 
the magnetic needle will be deflected so that its north pole 
will point toward the observer. 

The telegraph-sounder is a simple device for making use 
of the magnetic effect of the current. The diagram (Fig. 
164) will make plain the principle of telegraphing. 




Line 



., <T 




a' 
Earth Connection Earth Connection 

Fig. 164.— The telegraph. 

Suppose the electric current to flow from the battery 
through the apparatus at station X, and through the line wire 
connecting this with station Y, and through the apparatus 
at Y and back from a! to a through the earth. The electro- 
magnets c and c' will attract and hold down the springs e 
and e'. If, now, an operator at either station wishes to 
signal to one at the other station, he may separate the 
wires at b or b', when the magnets will cease to attract and 
the springs e and e' will fly up and click against the stops 
at d and d'. When the operator brings together again the 



256 



PHYSICS 



wires at b or V, the magnets will again pull down the 
springs e and e' upon themselves with a click. These clicks 
are made to represent letters, and thus the operators spell 
out words. The earth connections are made by gas or water 
pipes, or by metal plates buried in moist earth. The ex- 
pense of a second wire is thus spared and also its resist- 
ance, since the earth offers practically no resistance. In 
consequence, the required battery power is reduced just 
one half. In reality, the earth does not act as a return 
wire in completing the circuit, but simply serves to keep 
the earth terminals at the same potential. When this is 
the case, the effect on the circuit is the same as if the earth 
terminals were in direct contact with each other. 

The telegraph wires are usually strung through the air 
on poles, and must be supported on glass or porcelain insu- 
lators. In very large cities, however, there are ordinances 
against overhead wires, and the city circuits must conse- 
quently be underground. 

In this case the wires are insulated, usually with gutta- 
percha, and are laid in pipes, opening at regular intervals 
into more sizable manholes. The air lines were formerly 



b ;! 


e 


- C 

: 


1 Rnttpry 






Battery 



Fig. 165.— Single-stroke bell. 



Fig. 166.— Clatter bell. 



made of galvanized iron wire, but modern installations, 
both in Europe and America, are increasingly making use 
of copper wire, on account of its greater conductivity. 

The electric bell is a further application of the electro- 



ELECTRIC CURRENTS 



257 



magnet. In Fig. 165, suppose we close the circuit by 
bringing the wires together at b. This may be what is 
called a push button or a switch. The current will cause 
the electro-magnet to attract the spring e, which is fre- 
quently called an armature. As it descends it will strike 
the bell d. This arrangement is called the " single-stroke " 
bell. The " clatter bell " is arranged as shown in Fig. 166. 
When b is closed the spring 
e is drawn down by the mag- 
net, but the moment it leaves 
the stop at / the current 
ceases to flow, the magnet 
ceases to act, and the spring e 
flies upward against the stop 
/, only to be pulled away again. 
Thus it vibrates rapidly, and 
causes the bell d to clatter. 

The electric motor is another application of the electro- 
magnet. Fig. 167 shows how this electric current might 




Battery 

Fig. 167. — Electric motor. 




Fig 



Battery ~^^ 

168. — Electric motor. 



be used to make a wheel go around. This device is used 
for many purposes, and might be called a motor ; but Fig. 
18 



258 PHYSICS 

168 will explain in a very general way the principle usually 
employed in electric motors. Suppose an electric current 
passes around the magnet a, so as to make its right-hand 
end a north pole. Suppose, then, the current is led by the 
spring to the semicircular plate of metal e, borne upon a 
wooden disk, where it divides, half of it going about the 
coil c, so as to make it an electro-magnet with its upper 
end a north pole, and the other half of the current going 
about the coil d, so as to make its lower end a south pole. 
The current then returns to the semicircular metal plate/, 
and from that by the spring h to the coil b, the left-hand 
end of which it makes a south pole. It is manifest that c 
will be repelled from a and attracted toward b, and that d 
will be repelled from b and attracted toward a. As c passes 
by b the springs h and g will change to the opposite metal 
plates e and /. This will reverse the current in c and d, 
so that while the farther end of c is passing through the 




Fig. 169. — Electric motor 



lower half of its circular path it will be a south pole, and 
while the farther end of d is passing through the upper 
half of its circular path it will be a north pole. In other 



ELECTRIC CURRENTS 259 

words, the pole which is above will always be a north pole, 
and that below will always be a south pole. 

The arrangement by which the current is reversed at e 
and/ is called the commutator. These rotating magnets 
being fixed to an axis may cause other wheels to revolve, 
and thus set in motion a variety of machinery. The ac- 
companying figure (169) is more nearly the form of motors 
in use. It will appear again under the head of Dynamos. 

III. Electrical Measurements 

253. The Problem of Measurement is easy only when one 
has very definite ideas about what is to be measured. In 
the case of the electric current there are several measur- 
able aspects. We must begin with a very definite idea of 
these several aspects themselves. 

The thing we want to measure is manifestly motion, but 
the difficulty is that it is associated with something so alto- 
gether intangible and beyond our experience, that we are 
not able to call it matter, much less lay hold of it and 
determine its amount. Yet the best we can do is to con- 
sider the current as electricity in motion, and we must get 
some quantitative hold on it in order to study it at all 
scientifically. We must answer the question, " How much ? " 

The first thing that strikes us about electric motion is 
that it is quite independent of direction — goes up or down, 
right or left, north or south, wherever the conductor leads 
it, and apparently with equal facility. Matter does not 
behave in this free way, because it has weight. We can 
not ascribe weight, therefore, to electricity. Yet the two 
are alike in one respect. Matter falls to the earth, because, 
for it, that is the line of least resistance, and it is being 
urged on by gravitation. However little we know about 
electricity, we must believe that these same general prin- 
ciples hold, that electricity follows its own line of least 
resistance, and is urged on by some force quite as irresist- 
ible as gravitation. 



260 PHYSICS 

So much happens in the neighborhood of an electric 
conductor, that we are coming to believe that the real cur- 
rent is outside the conductor, and that the conductor sim- 
ply determines the direction of the current, pierces the 
ether in some way, and opens up a line of least resistance 
for the current to follow. In the same way we account for 
the force driving the electricity by assuming different elec- 
trical levels, or potential, and ascribing the driving force to 
difference of potential, or E. M. F. This clearly is one 
measurable aspect of electricity, and corresponds very closely 
to difference of level in the action of gravitation — as, for 
example, water pressure. A second measurable aspect is 
the resistance to the flow of the current. This may be 
compared to constrictions in the water pipe. The motor 
man when he turns on more or less current in his car does 
it by putting into the circuit less or more resistance, just 
as one may do in the case of the flow of water from a pipe 
opening more or less the stopcock at the faucet. A third 
measurable aspect of the electric current is the quantity 
that will flow through a conductor in a given time. This 
we measure by the work which it will perform. 

254. Ohm's Law. — There are two ways of affecting the 
quantity of water that may flow from a water pipe : one is 
to change the water pressure, the other is to change the 
size of opening in the faucet. Just so with the measure- 
ment of electric currents. Make the pressure or potential 
twice as great, and we make twice as much current flow ; 
make the resistance twice as great, and we reduce the flow 
of current one half. Three times as much potential, three 
times as much current ; three times as much resistance, one 
third as much current, etc. This is known as Ohm's Law, 
which may be stated as follows : The current varies directly 
as the potential and inversely as the resistance. If we 
represent current by C, potential or electro-motive force by 
E, and resistance by 7£, the formula which states this law 

w 

in brief form is, C ~ — . 
R 



ELECTRIC CURRENTS 261 

As was stated in section 242, the unit for electro-motive 

force is called a volt. (Named in honor of Alessandro Volta, 

1745-1872, born at Como, Italy.) It is very nearly the 

amount of pressure which is exerted by a Daniell cell (246). 

The unit of resistance is called the ohm. (Earned in honor 

of Georg Simon Ohm, 1781-1854, born at Erlangen, a town 

of Bavaria.) It is about the resistance offered by 39 feet 

of No. 24 copper wire. The unit of current is called an 

ampere. (Named in honor of Andre Marie Ampere, 1775- 

1836, born at Lyons, France.) It is about that current 

which a Daniell cell will send through 39 feet of No. 24 

copper wire. That is, it is the rate of flow which one volt 

can push through one ohm of resistance. (These units 

appear in the formula of Ohm's law thus : Amperes of 

Yolts of potential . T ^ . , , , ■ 

current =7^ , r . . .) It is measurable by its 

Ohms of resistance ' J 

chemical effects, magnetic effects, or heating effects. Let 
us take, for example, the chemical work which it may per- 
form. Any current which will decompose water and liber- 
ate 0.036 grams of hydrogen in an hour is a one-ampere 
current. The ampere will deposit 1.18 grams of copper 
from copper-sulphate solution in an hour. If the solution 
offers ten ohms of resistance, it will require an electro- 
motive force of ten volts to maintain a one-ampere current. 
If the electro-motive force is five volts, while the resistance 
is ten ohms, only a one-half-ampere current will flow, and it 
will require two hours for it to deposit 1.18 grams of the 
copper. If we have a ten-volt current and the resistance is 
five ohms, it will furnish a two-ampere current, and this 
will deposit 1.18 grams of copper in half an hour. 

Or we may take the heating effects as a measure of the 
current. If an incandescent electric lamp offers a resist- 
ance of 220 ohms, a potential of 110 volts will send through 

, ,- - ^ k x HO volts 

it one halt an ampere 01 current ; 0.5 ampere = ^- — j- — . 

Suppose this heats the filament sufficiently to make it give 



262 



PHYSICS 



a light equal to that of sixteen candles — this we call a six- 
teen-candle-power lamp. A thirty-two-candle-power lamp 
will require twice the amount of current, or one ampere, 
and we may produce it in one of two ways : First, we may 

A W 4.1. 14- 1 ' > 220 VOltS A 

double the voltage, 1 ampere = ^- — r — , or we may reduce 

the resistance one half, 1 ampere = j—^ — r — • But in any 

case the heat and light will be proportional to the amount 
of current which passes. 

255. The Tangent Galvanometer. — It is our custom, how- 
ever, to measure the current by its magnetic effects. It 
will be remembered that the galvanome- 
ter, Fig. 170, creates a magnetic field when 
the electric current passes around it (page 
255). We have a very simple means of 
measuring the amount of magnetic force 
developed in this field, and the magnetic 
force is a measure of the amount of elec- 
tric current which passes through the coil 
of the galvanometer; the needle is de- 
flected by the magnetic force of this helix through a cer- 
tain angle,' and it is found that the tangent * of this angle 

* In Fig. 171, let a e be a tangent to the circle ; 
a & is called the tangent of the angle aob, ac, 
a d, and a e are respectively the tangents of the 
angles ; a o c, a o d, and a o e. The length of these 
tangents is given in terms of the radius of the 
circle. In the figure a b is equal to the radius ; 
ac, ad, and a e are respectively two, three, and 
four times as great as the radius. By referring 
to the table of tangents, page 263. we may see 
that if the tangent of a o b is 1, the angle must 
be 45° ; the tangent of a o c being two, the angle 
must be about 64° ; likewise the angle a o d must 
be about 72°, and ao e about 76°. The law is that 
if a certain amount of current will deflect the 
needle from o a to the direction of o b, it will re- 




Fig. 170.— Tangent 
galvanometer. 




ELECTRIC CURRENTS 



263 



TABLE OF TANGENTS. 



Deg. 


Tan. 


Deg. 


Tan. 


Deg. 


Tan. 


1 


02 


31 


60 


61 


1.80 


2 


04 

05 


32 


63 


62 

63 


1.88 


3 


33 


65 


.... 1.96 


4 


07 


34 


68 


64 


2.05 


5 


09 


35 


70 


65 


2.15 


6 


11 

12 


36 


73 


66 

67 


2.25 


7 


37 


75 


2.36 


8 


14 


38 


78 


68 


2.48 


9 


16 

18 


39 


81 


69 

70 


2.61 


10 


40 


84 


2.75 


11 


19 


41 


87 


71 


2.90 


12 


.21 


42 


90 


72 


3.08 


13 


23 


43 


93 


73 


3.27 


14 


25 


44 

45 

46 .. 


97 

1.00 

1.03 


74 

75 


3.49 


15 


27 

29 


3.73 


16 


76 


4.01 


17 


31 


47 


1.07 


77 


4.33 


18 


33 


48 


1.11 


78 


4.71 


19 


34 


49 


1.15 


79 


5.15 


20 


36 


50 


1.19 


80 


5.67 


21 


38 


51 


1.24 


81 


6.31 


22 


40 


52 


1.28 


82 


7.12 


23 


42 

45 


53 


1 33 


83... 


8.14 


24 


54 


1.38 


84 


9.51 


25 


47 


55 


1.43 


85 


11.43 


26 


49 


56 


1.48 


86 


14.30 


27 


51 


57 


1.54 


87 


19.08 


28 


: .53 

58 


58 

59 

60 


1.60 

1.66 

1.73 


88 


28.64 


29 


89 


57.29 


30 


90 


Inf. 



varies as the current. For example, suppose we introduce 
into a battery circuit a galvanometer and a cell contain- 
ing copper-sulphate solution (Fig. 172) ; suppose also we 
find that copper is being deposited at the rate of 1.18 
grams per hour, and that the needle of the galvanometer 
is deflected to 83°. As has already been said, the amount 
of current which will deposit copper at that rate is called an 
ampere. Xow, it will be found that every time an ampere 
of current is passed through this particular galvanometer 



quire twice that current to deflect it to the direction of o c, and three 
times that current to deflect it to the direction of o d, and four times 
that current to deflect it to the direction of o e. 



264 PHYSICS 

its needle will be deflected to 83°. The tangent of 83° is 
8.14 (see table, page 263). If now we send through this 
circuit such a current as will deposit copper at one half 
the above rate, we shall find that the needle of the galva- 

Copper sulphate Galvanometer. 



Battery 



Fig. 172. 

nometer is deflected not to 41.5°, which would be half the 
angle, but to 76°, whose tangent is about half that of 83°. 
A current which would deposit one quarter as much cop- 
per would deflect the needle to 64°, whose tangent is one 
quarter that of 83°, etc. Thus a galvanometer which has 
been tested for some one known quantity of current may 
be very readily used, by aid of the table of tangents, to 
determine any amount of current which passes through it. 

A galvanometer used for measuring the quantity of cur- 
rent, or the amperes, is frequently called an ammeter, but 
galvanometers may also be arranged for measuring the 
electro-motive force, in which case they are called volt- 
meters. Since it follows from Ohm's law that G and E 
depend directly upon each other, whatever measures one 
practically measures the other also. 

Galvanometers used for voltmeters are usually con- 
structed with a coil of very large resistance — that is, the 
wire is long and very fine. The resistance is sometimes 
as much as several thousand ohms. The amount of cur- 
rent flowing through such an instrument is proportional 
to the E. M. F., and by observing the deflections produced 
by known currents, we may either standardize the galva- 
nometer by making the voltage directly on the graduated 
circle, or by preparing a reference table. As strong cur- 
rents would destroy such a fine coil, only tiny currents are 




ELECTRIC CURRENTS 265 

ever sent through it. This is managed by providing two 
paths for the current (Fig. 173) : one of low resistance, R, 
which will carry the major 
part, and the other of high 
resistance, r — that is, the gal- 
vanometer — to carry a very 

minor part. But since R and 

r are constant, the current FlG 173 

through the galvanometer, 

though very small, will always bear a direct relation to 
the whole current, and serve to measure it. 

It is manifest that if we know any two of the quantities 

E 

in the formula, 0= ^, we may calculate the third. It is 

manifest also that we must know the resistance through- 
out the entire circuit — that is, the internal resistance of 
the cell as well as the external resistance of the wires and 
galvanometer, and various pieces of apparatus used. We 
frequently designate the internal resistance by r and the 
external resistance by R. In which case, of course, the 

E 

formula becomes C = ^. 

r + R 

256. Resistance is a factor coming in at all times to re- 
duce current strength. One method of measuring it is by 
means of the AVheatstone bridge. 'This depends upon the 
principle that no current will flow between two points at the 
same potential, and that in any given uniform conductor, 
the fall of potential is also uniform. Suppose A B, Fig. 
174, to be a uniform conductor. In the first place, no cur- 
rent will flow at all if A and B are at the same potential, 
and a galvanometer introduced into such a circuit would 



Fig. 174. 



show no deflection. But if A is at higher potential than B, 
the fall of potential in passing from A to B will be uni- 



%66 . PHYSICS 

form. If the difference is three volts, any point C mid- 
way between A and B will differ from either by one and a 
half volt. 

The Wheatstone bridge is a uniform wire stretched 
between two fixed binding posts, and over a graduated scale 
which is provided with a sliding contact, dividing the wire 
into two determined portions. The action can best be 
understood by means of a diagram, Fig. 175. The current 
coming from the battery E divides at A into two portions, 
one taking the path AD B and the other the path A C B. 
If a galvanometer, G, is introduced between C and D, there 
will be no deflection if there is no current, and there will 




E 

Fig. 175. — Wheatstone bridge. 

be no current if C and D have the same potential. They 
will have the same potential if the resistance of A D bears 
the same relation to that of D B as the resistance of A 
bears to that of GB, or when 

AB:DB = AG:GB. 
If we substitute for A D the resistance to be measured, i£, 
and for D B some known resistance, W, we shall evidently 
be able to find some position for G such that no current 
will pass through the galvanometer. When this is the case, 
we have 

R : W = A G : G B, or R = ^ X W. 

Resistance Coils. — The known resistance W is usually 
supplied by means of a standard set of coils. They are 



ELECTRIC CURRENTS 



267 



made of German silver, with their ends soldered to solid 
pieces of brass on the top of the box. When all the plugs 
are in place, the current passes through the solid brass, and 

meets comparatively no resist- 
ance. When a plug is re- 
moved, the current must pass 
through the wire beneath, and 




Fig. 176. 



Fig. 177. 



so meet the corresponding resistance (Figs. 176, 177, and 
178). A very common way to measure resistance is to 
place the battery, galvanometer, and object whose resistance 
is to be found in circuit. Note the deflection of the gal- 
vanometer needle, then put the standard resistance coils in 
the place of the object whose resistance is to be determined, 
and throw into circuit enough resistance to bring the gal- 
vanometer needle to the 
same point as before. 
The resistance, which 
may now be read from 
the standard coils, is the 
resistance which was 
sought. 

Eesistance increases 
with the length of the 
conductor, and in the 
case of wires is greater 
the smaller the wire. Sil- 
ver, copper, and brass, being good conductors, offer the 
least resistance. In general the resistance increases with 




Fig. 178. 



268 



PHYSICS 



the temperature in the case of metals, but decreases in the 
case of carbon. 

The following list shows the resistance of certain metals 
compared with copper, the length, thickness, and temper- 
ature being the same for all : 



Copper 100 

Aluminium 246 

Zinc 446 

Platinum 630 



Iron 662 

Tin 738 

German silver 1228 

Lead 1462 



257. Arrangement of Battery Cells. — If a battery consist 
of n cells, and we connect them in series (247), we shall 
have 

because the potential differences E and the 
internal resistances r are propor- 
tional to the number of cells. 





Figs. 179 and 180.— Arrangement in series. 

The same battery joined in parallel (247) would give : 

E 



C 



(2) 



+ R 



since we really form one giant cell, whose E. M. F. is the 
same as a single cell, but whose internal resistance is reduced 
in proportion. 



ELECTRIC CURRENTS 269 

We reduce this last formula to the expression 

0=-^ (3) 

r + nR v ' 

To give this fraction the greatest possible value, and 
therefore make (7 a maximum current, we may either in- 
crease the numerator or diminish the denominator. Com- 




Figs. 181 and 182.— Arrangement in parallel. 

paring (1) and (3) we see that they have the same numer- 
ator, n E. The whole question turns then upon the value 
of the denominators. One is nr -\- B, and the other 
r-\-nR. If r is less than B, we can better afford to mul- 
tiply r by n, and so we choose the first arrangement in 
series. But if r is greater than B, we can better multiply 
i?, and we choose the arrangement in parallel. 

258. Divided Circuits. — It often happens that a conductor 
divides and offers two paths to the current. This happens, 
indeed, every time a battery is joined in parallel. The con- 
ductor divides into as many separate paths as there are 
cells. In all such cases the current also divides and trav- 
erses all the paths offered. If they have equal resistance, 
each path gets the same amount of current, but if they 
have unequal resistance, each path gets an amount inversely 
proportional to its resistance. 

The inverse of resistance, — , is conductance. The total 

r 

conductance of the system must evidently be the sum of 

the separate conductances. 



270 



PHYSICS 



The circuit branching off from a main circuit is called 
a shunt. 

If a current divides into two or more paths, it may be 
shown that the sum of the separate currents equals the 
main current. If, for example, in Fig. 183, the current C 




CuSo. 



Fig. 183. 



CuSo+ 

Divided circuit. 



is divided into two currents, c' and c" , and copper-sulphate 
cells be introduced into the main circuit and into each of 
the branches, the weight of copper deposited by C will just 
equal the sum of the weight deposited by c x and c 2 . The 
same result would have been shown by galvanometers, or 
any other form of ammeter or voltmeter. 

IV. INDUCTION 

259. Methods of Induction. — Induction is applied in elec- 
tricity, as well as in magnetism, to cover all action at a 
distance. But this means, in reality, all action confined to 
the surrounding medium, to the ether. Induction were 
better defined, therefore, as action between bodies without 
contact, and solely through the mechanism of the ether. 
Defined in this broad way, induction covers all ether stress 
— magnetic, electric, or gravitational. 

One can not move through an ordinary apartment with- 
out more or less disturbing every particle of air in the 
apartment. The more rapid the movement, the greater 
the disturbance. A circuit of copper wire is equally sensi- 



ELECTRIC CURRENTS 



271 



tive to changes in the snrronnding "field." No matter 
how brought about, the conductor responds to every change, 
and the induced current, like the air disturbed, is propor- 
tional to the rapidity of the change. 

These changes in the electric field may be brought 
about by the motion of a magnet ; by a field of varying 
strength ; by the movement of a conductor through which 
a variable current is flowing ; by the motion of the con- 
ductor itself in which the current is to be induced ; or, 
finally, by any combination of these five variables. They 
can best be studied experimentally. 

260. Induction by a Magnet. — If we take a coil of wire 
wrapped on a hollow spool, and connect the ends of the 
coil with a sensitive galvanometer, no current flows so long 
as the surrounding field remains the same. If, however, a 




Fig. 184.— Current induced by magnet. 



bar magnet be thrust into the center of the coil, the galva- 
nometer will show an immediate deflection. The magnet 
has no power except when in motion, for if allowed to 
remain quietly inside the coil the galvanometer needle comes 
to rest again and indicates no current. When the magnet 



272 PHYSICS 

is withdrawn, the needle swings in the opposite direction, 
showing a second induced current. We find that the more 
rapid the motion of the magnet, the greater the deflection 
of the needle. 

Instead of moving the magnet bodily, we may alter its 
intensity, and so produce the same series of induced cur- 
rents. This is conveniently done by introducing an elec- 
tro-magnet into the center of the coil. On making or 
breaking the current we get induced currents in opposite 
directions, surging through the coil and galvanometer ; but 
so long as a uniform current circulates through the electro- 
magnet, the field remains constant and no induced current 
passes through the galvanometer. 

-We might combine these conditions and have a movable 
magnet of variable strength. Or we might make the con- 
ductor itself approach or recede from a fixed magnet, 
either constant or variable, and so induce a current in the 
conductor. 

Whatever combination we use, the induced current de- 
pends upon the amount and rate of change in the magnetic 
field. Practically the current depends upon the number of 
lines of magnetic force cut in one second. Hence the mag- 
net may move or the conductor may move, or both may move ; 
or both may remain fixed bodily, and the lines themselves 
may move. The relative motion is the essential thing, and 
the greater the motion the stronger the induced current. 

261. Induction by Varying Currents. — Since all currents 
are surrounded by magnetic whirls, we may substitute a 
current for the magnet in any or all of the above experi- 
ments. 

Eemoving the iron core from the electro-magnet, the 
corresponding coil — which for convenience may be distin- 
guished as the primary coil — may be thrust into the sec- 
ondary coil and withdrawn, producing induced currents in 
opposite directions, just as in the case of the magnet (Fig. 
185). If the primary coil remains within the secondary 



ELECTRIC CURRENTS 



273 



coil, and the primary current be made and broken, we shall 
have corresponding induced currents in the secondary coil. 
Similarly, if the primary coil remain fixed and the current 
constant, induced currents may be produced by the motion 




Fig. 185. — Currents induced by varying currents. 

of the secondary coil. Furthermore, the parallelism be- 
tween induction by currents and induction by magnets is 
completed by the fact that here again the strength of the 
induced current depends upon the amount and rate of 
change in the primary field. 

262. Direction of Induced Currents. — The currents in the 
secondary coil vary in direction according to the conditions 
under which they are produced. We distinguish them as 
direct and inverse currents. Those are direct which so 
flow that they would give to the magnet, were it a core of 
soft iron, a magnetism of the same polarity that it now 
possesses. Those currents are inverse which flow in an 
opposite direction. When the field is increasing in strength, 
the induced currents are all inverse. When the field is 
diminishing, the induced currents are direct. 

263. Strength of Induced Currents. — Just as the direc- 
tion of the induced current depends upon the conditions 

under which they have been generated, so, then, strength 
19 



274 



PHYSICS 



depends upon the conditions. In a circuit of given resist- 
ance, the strength of the induced current depends solely 
on the electro-motive force, and this in turn depends solely 
upon the number of lines of magnetic force cut in one sec- 
ond. The voltage of an induced current is therefore in- 
creased (1) by increasing the magnetic field — that is, the 
number of lines ; (2) by increasing the rate at which these 
lines are cut— that is, the speed ; and (3) by increasing 
the length of the conductor— that is, the number of turns 
of wire. 

264. The Induction Coil is a simple and effective device 
for producing induced currents of very high electro-motive 
force, by increasing the number of turns of wire in the sec- 
ondary circuit. It consists of a central primary coil of 
short thick wire with a soft iron core, surrounded by a 
secondary coil of long, fine wire (Fig. 186). The primary 




Fig. 186. — Induction coil. 

circuit contains a current-interrupter, for rapidly mak- 
ing and breaking the current, and so inducing a rapid 
succession of inverse and direct currents. It acts upon 
the same principle as the interrupter used with the elec- 
tric bell. (See Fig. 166,/.) The coil is generally mounted 
on a hollow wooden base, which contains a condenser 
made of alternate layers of tin foil and paper saturated 
with paraffin, and connected with the primary circuit. 



ELECTRIC CURRENTS 275 

The action of the condenser is to dispose of the currents 
which are self-induced in the primary coil on breaking the 
current (see next paragraph), and so avoid the spark at the 
interrupter. The object of having the primary coil made 
of stout, short wire is to reduce resistance and so increase 
the quantity of the primary current. The secondary coil 
is made tremendously long. In the case of Mr. Spottis- 
woode's famous coil, it is 280 miles long, and gave a spark 
-42 cm. long. The very large voltage of the induced cur- 
rent enables it to overcome the great resistance of the air, 
and so give us these flashes of miniature lightning. 

"When provided with a condenser the induction coil is 
known as Ruhmkorff's coil. 

265. Spark Coil and Electric Gas Lighting. — When a 
current passes through a single coil of wire we have mani- 
festly a series of parallel circuits made by the successive 
turns of the wire, and all the phenomena of induced currents 
take place in and about the single wire whenever the cur- 
rent itself is made or broken. On making the current, the 
induced current is inverse, and consequently the only effect 
is to retard the establishment of maximum current in the 
circuit. But, on breaking the current, the induced current 
is direct and has the effect of prolonging the flow. While 
this " extra current," as it is called, is most noticeable in 
the case of circuits containing coils, it is a self-induction, 
which shows itself in all circuits, and produces the spark 
whenever the current is broken. This principle — provided 
against by the condenser in the Ruhmkorff coil — is made 
serviceable in the spark coil, used in electric gas lighting. 
The core is made of a bundle of iron wires, and the coil, in 
this case single, consists of many turns of moderately thick 
wire. The introduction of such a coil into a circuit provides 
a good strong spark, which conveniently takes the place of 
a match, at any point where the circuit may be alternately 
made and broken. The spark which appears in a " clatter " 
bell (Fig. 187) at the point/ where the current is alternately 



276 



PHYSICS 




made and broken is due to the induced current. The spark 
is evidence that the induced current has high voltage. 

This spark will light the gas. 
If one touches the conductor 
on both sides of this point, 
/, thus making it possible for 
this induced current to pass 
through his body rather than 
the air, he will feel a slight 
shock, particularly if he 
moistens his hands and uses 
metal handles to make better 
contact. The dry outer skin 
being a poor conductor, the tongue or inner surface of the 
mouth may be used to furnish a place for contact. 

266. The Telephone.— Fig. 188 will serve to illustrate 
the essential features of the telephone. The transmitter, 
I 7 , is a box filled with granules of carbon, into which the 
battery wires enter. P is the primary circuit of an induc- 
tion coil. Tapping upon the box, T, or speaking into its 
causes the battery current to vary in strength. These 
variations in the primary circuit cause a secondary current 
of high intensity to surge to and flow through the secondary 
coils, S and 8\ and around the permanent steel magnets, 




Fig. 188.— The telephone. 




m and m'. When these induced currents go in one direc- 
tion they strengthen the magnet, and when they go in the 
opposite direction they weaken the power of the magnet. 



ELECTRIC CURRENTS 277 

This causes the disks of soft iron, R and R', to vibrate 
exactly as they would if one spoke directly against them, 
and, strange to say, if one of these receivers, R or R\ is held 
near to a person's ear, this vibration will reproduce the 
sounds which are made by a voice speaking into the box of 
the transmitter, T or T'. 

267. Transformers. — If the electric current is to be con- 
ducted far, as, for example, to light dwellings several miles 
away from the central station where the electricity is pro- 
duced, it must have high voltage to push its way through 
the long conductors. The voltage will probably need to be 
so high as to be a deadly current. Before receiving this 
into our houses, we would prefer to have its voltage reduced. 
This is done by transformers which are simply induction 
coils. What we lose in voltage in this way we gain in 
quantity, as might be expected from what we know of the 
conservation of energy. Transformers of the induction 
coil type require alternating currents. They consist of an 
iron core, a primary coil, and a secondary coil. The ratio 
of the electro-motive force in the primary coil to that in 
the secondary coil is known as the ratio of transformation. 
This may be either up or down — that is, the voltage may 
be either raised or lowered. As this depends upon the 
number of turns of wire in the two coils, the ratio of trans- 
formation is practically the ratio of the number of turns of 
wire in the primary coil to the number of turns in the sec- 
ondary coil. If, for example, an external circuit has a pres- 
sure of 3,000 volts, and we wish a house current for incan- 
descent lamps under a pressure of but 100 volts, the ratio 
will clearly be 30 and the coils will be wound accordingly. 
In a closely peopled district the transformer may be at the 
entrance to the town, while in a more scattered district the 
transformer may be in each house. 



278 



PHYSICS 



V. Electric Currents by Mechanical Means 

268. The Magneto-Electric Machine. — Faraday followed 
up his discovery of current induction in 1831 by the inven- 
tion of a magneto-electric machine. It consisted of a cop- 
per disk mounted to rotate between the poles of a per- 
manent horseshoe magnet. The current generated in the 
disk was collected by strips of copper pressing respectively 

against the axle and the circum- 
ference of the disk. This little 
machine is the honorable ancestor 
of all the company of machines, 
great and small, magnetos and dy- 
namos, that have since been invent- 
ed for the purpose of turning me- 
chanical motion into electric energy. 
It is the simplest combination pos- 
sible of the two essential elements, 
a magnetic field and a movable con- 
ductor. 

Later machines substitute a coil 
of wire, an " armature " for the disk. 
A simple form of this is presented in 
Fig. 189. It is manifest that the 
current is produced in this machine 
by causing a helix of wire to alter- 
-Magneto-eiectric na t e l y approach and recede from a 

machine. J rr 

steel magnet. The current thus 
induced has high potential. It is used by physicians in 
treating patients by electricity. Its more common use is 
for telephone calls. 

269. The Dynamo. — It was early realized that no field 
magnet, of steel could be so powerful as an electro-magnet. 
In the dynamo this field electro-magnet is energized by 
means of the current generated by the machine itself. 
This is possible by reason of the residual magnetism which 




Fig. 189.- 



ELECTRIC CURRENTS 



279 



is found to inhere in the iron core of the field magnet. 
The field thus produced is very weak, but it is not without 
effect. When the armature rotates in this field, very feeble 
currents are set up. These pass into the external circuit 
and through the coils of the electro-magnets, thus strength- 




Galvanometer 

Fig. 190.— The dynamo. 

ening the magnetic field, which in turn induces stronger 
currents in the armature. By this cumulative process the 
field soon mounts to its maximum strength, and the 
machine generates a powerful current. 

The principle of the dynamo may be illustrated by Fig. 
190, which will be recognized as very closely resembling 
Fig. 168, used to illustrate an electric motor. A galva- 
nometer has been substituted for the battery, to indicate 
the current which this will produce. The electro-magnets 
a and b are the field magnets, and the electro-magnets c 
and d are the armatures. The iron cores of these electro- 
magnets are never entirely without magnetism, hence if we 
cause c and d to rotate, when they approach b and a they 
will induce reverse currents in the wires which encircle 
these cores, and when they recede from b and a they will 
induce direct currents in these wires. This would result in 



280 



PHYSICS 



an alternating current if it were not for the commutator 
(see pp. 259 and 281). 

All dynamos consist essentially of three elements : 

1. The magnetic field. 

2. The armature. 

3. The collecting apparatus. 

a. Commutator in the direct-current machines. 

b. Collecting brushes in the alternating-current ma- 
chines. 

The Magnetic Field. — The smaller dynamos have a 
simple field produced by two pole pieces of opposite polar- 
ity, facing each other. Each pole piece is hollowed out 
into a semi-cylinder, and as the two pieces almost touch 
each other, the armature rotates in a nearly closed cylinder 
of highly magnetized iron (Fig. 191). 




Fig. 191.— The dynamo. 



The powerful modern dynamos are frequently multi- 
polar, having four, six, or even eight pole pieces. 

The armature in all modern machines is made up of 
many circuits. The single-coil armature can not give a 



ELECTRIC CURRENTS 281 

steady current, because at each reversal of current — that is, 
twice every rotation — the current must be reduced to zero, 
and consequently the current in the external circuit is in 
reality a series of momentary currents, all in the same 
direction but not continuous. By having several separate 
circuits moving in different parts of the field, we shall 
always have one or more of them current-producing, and 
consequently in the external circuit, though the current 
is still subject to pulsations, it never entirely dies away. 
It is also possible to cut out the separate circuits when 
they are not active, and so reduce the resistance of the 
armature. 

The Collecting Apparatus — The Commutator. — When 
the current desired must be direct, the collecting brushes 
have the added function of changing the alternate currents 
into a direct and continuous one. The simple commutator 
has already been described in connection with the electric 
motor (page 259). 

By referring to Fig. 190, we may see how these brushes 
serve to change an alternating current into a direct one. 
Suppose c and d to be approaching o and a respectively. 
Currents will be induced in the wire encircling these cores 
which will take the direction of the arrows — that is, a cur- 
rent will be induced which will pass around c from f to e 
and around d from f to e. These currents will combine 
and pass out by the spring or " brush," g, around the core 
a so as to intensify its magnetism, through the galvanom- 
eter, whose needle it will deflect, showing at the same time 
the direction and the strength of the current, then around 
b so as to increase its magnetism, and finally back to / by 
the spring or " brush," h. When c and d pass b and a and 
begin to recede from them, the current which encircles 
them will be induced in the opposite direction, but at the 
same instant the brushes shift to the opposite plates, e com- 
ing under h and /coming under g. So that the moment 
the magnets c and d require the current to pass from e to/, 



282 PHYSICS 

e comes in contact with li and / with g, and thns the current 
continues to flow from h to g as before. Of course, it is 
understood that e and / are semicircles of metal upon a 
wooden disk, so that the only way the current may pass 
from / to e is through the wires which encircle the cores 
c and d. 

In the case of alternate-current machines, the brushes 
have only to collect the current and send it over the main 
circuit. Alternators are very much used in electric light- 
ing. The current surges back and forth so rapidly through 
the lamp as to produce a steady light. They have the 
advantage of requiring no commutator. The Westinghouse 
machine is the one best known in America. 

The total output of electric energy in any machine is 
equal to the product of C and E or C E Watts, and this 
divided by 746 will give the equivalence in horse power. 
The mechanical efficiency is the ratio of the total output 
of energy to the energy put into the dynamo in the form 
of mechanical work. It must be remembered that we never 
get out of any machine as much as we put into it. We use 
a steam engine or water power to cause the dynamos to go ; 
a 60-horse-power steam engine can not produce electrical 
energy through the dynamos which will do the work of 60 
horse power. Electricity is not to be regarded as a source 
of power. It can not be called a rival of steam, since we 
are dependent upon steam to produce it. Its use is to 
transmit the power of the steam engine, and hence, if it is 
the rival of anything, it is the rival of the engine belt. A 
short time ago most of the street cars in New York city 
were cable cars — that is, they ran by grappling a cable, or 
huge engine belt, which ran from a central steam engine 
for many miles in a conduit under the street. This cable 
was not the source of power ; it only transmitted the 
power. But more recently electricity has been adopted as 
a successful rival to this cable as a means of transmitting 
the power of the central steam engine. The engine is still 



ELECTRIC CURRENTS 283 

the power which moves the cars, but instead of pulling 
them along now by means of a very long cable passing 
around the driving wheel of the engine and for miles under 
the street, the engine now operates dynamos, and the dyna- 
mos send the current through conductors running in con- 
duits under the street where the cable used to run. The 
cars receive the electric current from these conductors 
through motors underneath each car, which are geared to 
the car axle. Whenever the motorman turns the electric 
current upon a car to make it go, it throws a load upon the 
central steam engine just as much as the cable did ; and 
when the electric car goes up hill it throws an extra load 
upon the engine, just as the cable did ; and when the elec- 
tric lights or the electric radiators in the cars are turned 
on, the central engine does a definite additional amount of 
work, which requires a definite additional amount of coal 
to be burned just as truly as though the cars were heated 
by steam or lighted by coal gas. If the dynamo current is 
used to ring an electric bell, or decompose water, or do 
work of any kind, the dynamo goes harder and the steam 
engine goes harder. More steam must be produced and 
more coal burned to just the extent of the work per- 
formed. 

Electricity is the most convenient method of transmit- 
ting power. It will go over hill, through dale, up and down, 
right and left, and may be tapped wherever you will. It 
has now become the most economical method as well. The 
more carefully the current is studied, the more wisely are 
we able to make use of it. In any circuit the loss of energy 
appears as heat. By sending currents of excessively high 
voltage, as much as 10,000 volts or more, with current 
strength of only a few amperes, this loss is made compara- 
tively trifling. When the current has reached the place 
where it is to be used, its character may be changed, as 
desired, from alternating to direct, and from high voltage 
to low voltage, with proportionally increased quantity. 



284 PHYSICS 

• 

As time passes, the water powers of the country are 
being increasingly harnessed to the work of current genera- 
tion, and the current is being transmitted over long dis- 
tances. At the Frankford Electrical Exhibition a current 
of 140 horse power was brought 117 miles from the Falls of 
the Necker with a loss of only 26 per cent. It is also quite 
possible that we may speedily find it more economical to 
burn our coal at the mines themselves, and send the energy 
to town over copper wires instead of in railroad cars. 

The usefulness of the current depends very largely upon 
the fact that it may readily be transformed into mechan- 
ical motion again by means of the electric motor. In the 
dynamo we put in mechanical energy and get out electric 
current ; in the motor we put in current and get out me- 
chanical motion. Dynamo and motor are thus the converse 
of each other. They are, indeed, entirely interchangeable. 
A dynamo fed with current becomes a motor ; a motor fed 
with mechanical motion becomes a dynamo. 

VI. Electkic Currents produced by Heat 

270. Thermo-electric Currents. — When the junction of 
two dissimilar metals, such as antimony and bismuth, is 
heated and their colder ends are connected by a copper 
wire, a current is found to flow in the wire from the anti- 
mony to the bismuth. When several such pairs are united 



r 1 1 1 'i 1 1 r. i i- 





Figs. 192 and 193. 

in series, and the alternate junctions heated, the resulting 
thermo-electric current is proportional to the number of 
pairs (Figs. 192 and 193). 



ELECTRIC CURRENTS 285 

271. The Thermopile is a compact bundle of such anti- 
mony-bismuth pairs, sometimes as many as thirty-six, and 
when connected with a sensitive galvanometer forms a 
wonderfully delicate means of detecting and measuring the 
slightest differences of temperature. It is with this instru- 
ment that we explore the spectrum and measure the com- 
parative temperature of the various rays. Thermopiles are 
now manufactured and sold, which are a very practical 
means of furnishing electric currents for laboratory and 
lecture-room work. 



LIGHT 

CHAPTER XXVI. — Rays of Light in Straight Lines 

272. What is Light? 

273. How the Velocity of Light was determined. Fig. 194. 

274. Some Results of the Fact that it takes Light Time to Travel. 

275. The Sources of Light. 

276. Photometry — Law of Inverse Squares. Figs. 195 and 196. 

277. The Relative Illumination of a Page of Reading Matter when 

held near to or far from the Source of Light. 

278. Relation between Temperature and Intensity of Light. 

279. The Visual Angle. How we use it for estimating Distances. 

280. Shadows. Figs. 197 and 198. 

281. The Moon's Shadow. Eclipses of Sun and Moon. Figs. 199, 200, 

and 201. 

282. Light through Small Apertures. Fig. 202. 

CHAPTER XXVII.— Reflection of Light 

283. Laws of Reflection. Fig. 203. 

284. Images in Plain Mirrors. Figs. 204 and 205. 

285. Concave Mirrors. Principal Focus and Conjugate Foci. Figs. 

206 and 207. 

286. Enlarged Images formed in Concave Mirrors. Fig. 208. 

287. How an Inverted Image is formed in a Concave Mirror. Fig. 209. 

288. Diminished Images formed in a Convex Mirror. Fig. 210. 

289. A Silver Spoon as a Concave and a Convex Mirror. 

290. A Curved Image from a Straight Object. 

CHAPTER XXVIII. — Miscellaneous Observations on Reflection 

291. How Daylight is diffused. 

292. Halos about Street Lights and the " Circle around the Moon." 

293. " The Sun drawing Water." 

294. Illumination of Clouds at Sunset. 

295. Moonlight and the Phases of the Moon. Fig. 211. 

296. How the Dark Part of the New Moon is made Visible. 

297. Why are Transparent Objects and very good Reflectors so nearly 

Invisible Themselves f Figs. 212 and 213. 

287 



288 PHYSICS 

298. Visibility of Print upon Glazed and Unglazed Paper; Drawings 

upon Rough and upon Highly Polished Surfaces. 

299. Twilight. Fig. 214. 

CHAPTER XXIX.— Refraction of Light 

300. Refraction of Light denned and illustrated. Fig. 215. 

301. Index of Refraction. 

302. Cause of Refraction. Fig. 216. 

303. Value of the Index. 

304. The Critical Angle. Fig. 217. 

305. Total Reflection. 

306. Applications. Figs. 218, 219, 220, and 221. 

307. Refractions in Prisms. Fig. 222. 

308. Enlarged Images produced by Refraction. Fig. 223. 

309. Different Kinds of Lenses and the way they refract Light. Fig. 

224. 

310. Inverted Images produced by Refraction. Fig. 225. 

311. The Path of Rays of Light exhibited by Crayon Dust. Measuring 

the Focal Distance of a Lens. Fig. 226. 

312. Pictures formed at the Focus of a Lens. 

313. How a Lens forms a Picture. Fig. 227. 

314. Material of Lenses. 

315. Familiar Illustrations of Lenses. 

316. The Simple Microscope. Fig. 228. 

317. Compound Microscope. Fig. 229. 

318. The Telescope. 

319. The Human Eye. Figs. 230, 231, and 232. 

320. The Spectrum. Figs. 233, 234, and 235. 

321. The Invisible Spectrum. 

322. Complimentary Colors. Fig. 236. 

323. Fluorescence and Phosphorescence. 

324. Temperature and Color. 

325. Rontgen Rays. Figs. 237 and 238. 

326. Hertz Rays. 

CHAPTER XXX.— Polarization of Light 

327. Transverse Vibrations. Fig. 239. 

328. Polarization of Light. Figs. 240 and 241. 

329. Applications of Polarized Light. 

330. Rotation of the Plane of Polarization. 

331. The Identitv of the Various Forms of Radiation. 



CHAPTER XXVI* 

RAYS OF LIGHT IN STRAIGHT LINES 

272. What is Light ? — We know that sunlight tans the 
skin and fades the colors in our clothes, while at the same 
time it causes the brilliant colors of the flowers. It makes 
the green color in plants, for potatoes sprout and grow 
white vines in a dark cellar, but green ones in the open 
sunlight. It assists the healthy growth of most plants 
and animals, but hinders the growth of molds and many 
obnoxious germs. Milk pans, butter pots, bread jars, bed- 
ding, etc., are put out to "sun" in order that they may 
become " sweet." Sunlight is the most efficient disinfect- 
ant for our apartments. Yet, what is this light? We 
speak of its coming from an object and going to an object, 
and we know that it requires about eight minutes for light 
to travel from the sun to the earth, about forty minutes 
for it to come from the planet Jupiter, about four hours 
for it to come from the planet Neptune, and about forty 
years for.it to come from the North Star. Thus the 
velocity of light is 186,000 miles per second. This is also 
the velocity of electricity and of heat radiation. What- do 
we mean when we speak of light streaming into a room ? 
Is it a substance ? Has it weight ? Can it fill a space and 
exclude other things from the same space ? We naturally 
think of light as closely connected with heat. We are 

* Considerable portions of these chapters on Light have been taken 
from WoodhulPs First Course in Science, with the permission of the 
publishers, Messrs. Henry Holt & Co., New York. 

20 289 



290 PHYSICS 

familiar with the heating of substances until they give out 
light, first dull red, and afterward brilliant white light. 
We naturally think of both light and heat as being the 
essential characteristics of the sun's rays. In succeeding 
pages we shall learn how to concentrate the sun's rays by 
means of concave mirrors or convex lenses, so as to set fire 
to wood or paper. We shall also learn how, by means of 
prisms, to separate the light rays from the heat rays. 
They may be separated also by filtration or absorption, as 
has already been stated in sections 202 and 203. From 
this we may learn that while heat rays and light rays are 
very closely associated, they are not the same. Our pres- 
ent conception is that light rays, heat rays, and electric 
currents are all forms of ether vibrations, differing only in 
wave lengths. Those which are capable of exciting the 
optic nerve we call light rays ; they have the shortest wave 
lengths. Those which excite the nerves of temperature 
sensation we call heat rays ; they have medium wave 
lengths. Those which produce electric phenomena we call 
electric waves ; they are the longest of the three kinds 
mentioned here. These waves may readily be transformed, 
the one into the other, and all may set up those molecular 
motions in matter which we call heat. The distinction 
between these various kinds of ether vibrations will be 
made more clear in section 331. 

273. How the Velocity of Light was determined.— It was 
noticed by a Danish astronomer, Olaf Eoemer, in 1675, that 
the observed and computed times of the eclipse of Jupiter's 
satellites differed by an amount too great and too constant 
to be assigned to observational error. The eclipse of a 
satellite occurs, as we all know, when it passes into the 
shadow of its planet, and the precise time and duration of 
an eclipse may therefore be calculated with great accuracy. 
Eoemer noticed that when the eclipse was seen while the 
earth (Fig. 194, A) and Jupiter were on the same side of 
the sun — as the astronomers say, " in conjunction " — the 



RAYS OF LIGHT IN STRAIGHT LINES 



291 



time was 1(3' 36" earlier than when the earth (Fig. 194, B) 
and Jupiter were on opposite sides of the sun ; that is, " in 
opposition." In the latter case it is very plain that the light 
reflected from the satellite has to 
travel farther through space by just 
the diameter of the earth's orbit — 
about 184,000,000 miles. Dividing 
the distance by the time in seconds, 
we have a speed of about 186,000 
miles per second. Several more re- 
fined methods of determining the 
velocity of light have been employed, 
but all give about the same result. 

274. Some Results of the Fact that 
it takes Light Time to travel. — As a 
result of the appreciable time re- 
quired by light to pass over space, we 
see the celestial universe never as it 
is, but always as it ivas. Even the 
moon, our nearest neighbor in space, 
is over a second behindhand in all 
her reports, and the* sun is 8' 18" be- 
hind time. He is mathematically 
above our horizon by that amount of 
time before we see him at all, and he 
remains visible to us for the same 
length of time after he has really 
passed below the western horizon. 
Xow in eight minutes of time the 
earth will cover an angle of 2° in 
rotation. But the sun, as seen from 
the earth, only covers an angle of 
about half a degree. Consequently 
the sun is really four times his own 
diameter above the horizon before we know that he is up 
at all. (These calculations neglect refraction, Chapter 




Fig. 194.— The velocity 
of light. 



292 PHYSICS 

XXIX, section 306.) The reports from the distant planets 
are correspondingly retarded, but the delay is the most 
noticeable in the case of the fixed stars. The nearest one, 
a Oentauri, is so far off that it takes about three and a 
half years for its light to reach us. Sirius, the brightest 
star in our heavens, requires 16.7 years to send its light 
to us ; Arcturus 25.4 years ; Polaris, the North Star, 42.4 
years ; and o- Draconis 129.1 years — that is, if the last-men- 
tioned star should cease to send forth light to-day, it would 
be 129.1 years before its last light wave would reach us, 
although during each second in all that time it would have 
traveled toward us at the inconceivable speed of 186,000 
miles. 

275. The Sources of Light are practically the same as the 
sources of heat — the sun, chemical energy, mechanical power, 
and electricity. These agents all have the power of setting 
up ether vibrations of such rapidity that they are sensible to 
us as light. The one principle in all our artificial lights is 
the heating of matter to incandescence — that is, to such a 
temperature as will set the ether into vibration within the 
prescribed limits of light. In the case of candle, kerosene 
lamp, or gas flame, by far the largest product of the chem- 
ical action is heat. This heat raises a small portion of 
the more refractory particles of carbon to incandescence, 
and these are responsible for all the light. This is well 
illustrated by holding a small wire in the flame of a Bun- 
sen burner until it gets white hot. To gain the incan- 
descence needed a high degree of heat is required. We 
are obliged to spend much of our energy in producing 
the long vibrations in the ether that are of no direct use 
in illumination. It is very natural, therefore, that physi- 
cists should look to the possibility of producing the 
shorter ether waves, which affect our eyes as light with- 
out passing through the heat stage at all. Tesla especially 
has worked over this problem with much patience and 
ingenuity. 



RAYS OF LIGHT IN STRAIGHT LINES 293 

276. Photometry — Law of Inverse Squares. — The farther 
we get away from a light the less intense it becomes. Let 
a candle flame (Fig. 195) be the source of light. We can 
picture rays goiug out in all directions. Suppose we trace 




2 

o 

Fig. 195. — Law of inverse squares. 

the four rays which at any given distance, say one metre, 
bound a one-inch-square screen. As the rays come from a 
common center they are divergent, and the farther away we 
go, the wider apart do they become. At a distance of two 
metres let us place a second screen. By similar triangles 
each side of this second square must be twice as long as 
those of the first, and consequently the area must be four 
times as great as that of the first. If we remove the first 
screen, the amount of light that formerly fell on it is now 
distributed over four times the area, and consequently can 
be only one fourth as intense. If we place a third screen 
three metres away from the flame, each side of the square 
will evidently be three times as long as those of the first, 
and the area consequently nine times that of the first. If 
the second screen be now removed the original illumina- 
tion is spread over nine times the area, and consequently 
can be only one ninth as intense. The distances are, 
1:2:3; the areas, 1:4:9; the intensities, 1 : J : J. Hence 
the law of inverse squares : The intensity of light varies 
inversely as the square of the distance from the source. 
The law holds for gravitation, heat, and the attractions 
and repulsions of magnets and electrified bodies. In every 
case the force varies inversely as the square of the distance. 
The standard in America and Great Britain is the candle 
power. A standard sperm candle, weighing six to the 
pound, seven eighths inch in diameter, and burning 120 
grains an hour, gives 1 candle power ; an average gas jet 



294 



PHYSICS 



yields 10 candle power ; an incandescent lamp usually 16 
candle power ; the more powerful oil lamps as high as 60 
candle power ; and the usual arc lamps about 120 candle 
power. 

Photometry is a science of light measurement. It has 
both scientific and practical importance. Since light, like 
other commodities, is now bought and sold, people want to 
know how much they are getting or giving. An instru- 
ment for measuring the intensity of light is known as a 
photometer. We will consider only one. All methods of 
measuring light depend on the law of inverse squares. 

Rumford's Photometer. — If a vertical rod or other opaque 
object be placed in front of a screen (Fig. 196), and light 
from two sources fall upon the rod, it will cast two shadows 




Photometer. 



on the screen. Each shadow, however, will be illuminated 
by light coming from the other source. By having the 
shadows not too far apart, we may compare their intensities 
by the eye with fair accuracy. If the lights are placed at 
suitable distances, the shadows may be made equally intense. 



RAYS OF LIGHT IN STRAIGHT LINES 295 

As the illumination from both sources is now equal, their 
candle powers will be as the square of their distances from 
the screen. 

277. The Relative Illumination of a Page of Reading 
Matter when held near to or far from the Source of Light. 
— A kerosene lamp or a gas name may give a light of six- 
teen candle power, and when we reflect that not many years 
ago people used fewer candles than we now use of lamps or 
gas jets, it appears that we are more than sixteen times as 
well provided with light as our ancestors. They, however, 
usually held a candle very near to the page while reading, 
and people in these days often employ a poor lamp and sit 
far from it. One should frequently remind himself that 
when he is twice as far from the light he receives one quar- 
ter as much of it, and when he is three times as far away 
he receives only one ninth as much of it, etc. 

278. Relation between Temperature and Intensity of 
Light. — It is found that the intensity of the light proceed- 
ing from any given source increases remarkably with an in- 
crease in the temperature of the source. Authorities differ 
as to the temperature at which light waves begin to be 
given off, Weber placing it at 390° C. and Draper at . 500° 
C. It depends, of course, upon the sensitiveness of the 
observer, and we can never know absolutely. Ordinary 
solids must be heated from 800° C. to 1,000° C. in order to 
emit rays of white light — that is, to become white hot. 
But all observers agree as to the remarkable increase at the 
higher temperatures. It is estimated that platinum gives 
thirty-six times as much light at 1,400° C. as it does at 
1,000°. This fact is utilized in the incandescent electric 
lamp. The carbon filaments are heated just as hot as they 
may be without suffering too rapid disintegration. Econ- 
omy is found in the nice balance between these two con- 
siderations. The temperature of the " crater " of an arc 
lamp is about 3,500° C. Hence its large illuminating power 
and its economy. 



296 PHYSICS 

279. The Visual Angle : How we use it for estimating 
Distances. — The angle which the lines of light from the 
opposite extremities of an object make at the eye is called 
the visual angle. Our estimates of the size of things seem 
to be founded to a certain extent upon their supposed dis- 
tance and the visual angle which they subtend. This mar- 
velous faculty which we have of judging distance is un- 
doubtedly acquired by a slow process of education. The 
story is familiar of the person born blind who, having in 
later years obtained his sight through a surgical operation, 
reached out his hand to lay it upon a distant church steeple 
which he supposed to be near enough to touch. Subtend- 
ing so small a visual angle as it did, if he conceived its dis- 
tance so little, he must have thought it a miniature toy. 
One appreciates that this faculty can be trained when he 
sees how efficient sailors become in the use of it. The 
landsman finds himself greatly at loss to estimate distances 
upon the sea. 

If we can form no conception of the distance of an 
object, we are at a loss to make any estimate as to its size. 
People sometimes amuse themselves making comparisons 
between the apparent size of the moon and that of familiar 
objects. One says it looks about the size of a silver dime, 
another compares it to a silver dollar, and still a third finds 
a carriage wheel represents it. How completely without 
foundation these estimates are will be seen when one con- 
siders that if the eye were placed at one end of a metre 
stick, and an object one centimetre in diameter were placed 
at the other end, it would subtend about the same, visual 
angle as the moon. 

Some curious errors of judgment as to size occur when 
we have formed a wrong estimate of the distance of an 
object. In the dim twilight, one evening, a cat shot across 
the field of vision and ran up a little tree not more than 
four rods distant from the observer, who had not noticed 
the little tree because a very large tree about twice as far 



RAYS OF LIGHT IN STRAIGHT LINES 297 

. distant stood directly in line with it. Supposing, therefore, 
that the cat was twice her actual distance away, he was at 
the moment rather appalled at the apparition of a cat 
three feet long instead of eighteen inches, as she probably 
was. Such hallucinations are apt to fade from the mind as 
suddenly as they come. 

The sun and moon each subtend a visual angle of about 
half a degree. The sun is about four hundred times as far 
away as the moon, and is about four hundred times as broad. 
Yet they appear to us to be about the same size, because 
we conceive of them as being at the same distance. If by 
any means we could make the sun appear to be farther 
from us than the moon, it would appear larger. To most 
persons the sky appears like a flattened dome, with the 
zenith much nearer than either horizon. Hence the sun 
and moon appear to us larger when in the horizon than in 
the zenith. 

The sun is so far away that the rays of its light which 
reach us are very nearly parallel. The greatest possible 
variation from parallel would obviously exist between those 
rays which start from opposite extremities of the sun's disk 
and meet at the eye of the observer. Such rays would vary 
half a degree from parallel. 

An object becomes invisible when it subtends a smaller 
angle than ¥ J, 7 of a degree. If it is one of the largest bodies 
in the universe, but far enough distant to subtend ^| ¥ 
of a degree, it is invisible without the aid of a telescope ; 
or if it is ever so near at hand but subtends so small an 
angle, it is invisible without the aid of a microscope. These 
instruments increase the visual angle by means of lenses, 
as will be explained in Chapter XXIX. 

We are deceived with reference to the size of an object 
if it gives a very brilliant light. The filament in an incan- 
descent electric lamp, which is so small as to be seen with 
difficulty when it is not giving light, appears very much 
larger when it is giving light. The sun, although it sub- 



298 PHYSICS 

tends the same visual angle as the moon, appears larger 
because it is more brilliant. When the sun is seen through 
a thin cloud which shuts off some of its light, persons are 
often surprised to find that it appears smaller than they 
had imagined. 

280. Shadows. — In Fig. 197 let L represent a point of 
light, cd an opaque object, and ef a screen. It is manifest 
that no light from L will pass into the region c d ef. This 
is the shadow. Its length may extend indefinitely as the 
screen is moved away from c d. We more often think of 
the shadow as being mere- p 

ly that portion of the screen y<^\ 

which receives no light. 





Fig. 197. — Umbra. Fig. 198.— Umbra and penumbra. 

Umbra and Penumbra. — In Fig. 198 let F represent a 
flame, and let a and b represent its extremities ; c d is an 
opaque object, and ef a screen as before. The region into 
which no light may pass is cd g li. Around this there is 
a region ceg and dfh into which a more or less limited 
portion of the light from F may pass. To distinguish 
between these regions, we call the portion which receives 
no light the umbra, and the other the penumbra. The 
penumbra grows gradually denser as we pass from its outer 
limits inward toward the umbra, and there is no distinct 
dividing line, as eg or dh. 

281. The Moon's Shadow— Eclipses of the Sun and 
Moon. — In Fig. 199 the angle a o b is made just half a de- 
gree. If an observer were stationed at o, and the lines oa 
and o b were extended 240,000 miles (the distance of the 



RAYS OF LIGHT IN STRAIGHT LINES 

moon), they would then be just far enough apart to 
span the moon — that is, 2,000 miles apart. If then 
they should be extended 92,500,000 miles (the dis- 
tance of the sun), they would be far enough apart to 
span the sun — that is, 860,000 miles apart. 

If it were strictly true that both the sun and 
moon subtend an angle of half a degree, it would 
follow that the moon's shadow as cast by the sun 
would be just long enough to reach the earth. The 
truth is that the moon's umbra is sometimes a little 
longer than its distance from the earth, and it cov- 
ers a small portion of the earth's surface when it 
chances to sweep across it. Usually, however, we 
pass through nothing but the penumbra on an occa- 
sion of an eclipse of the sun. 

The umbra has the shape of a cone, whose length 
is about 240,000 miles and whose base is about 2,000 
miles. The penumbra is also an exceedingly slim 
cone, whose base is removed to an indefinite dis- 
tance, and whose apex is cut by the umbra, which 
extends into it like the crater of a volcano. Fig. 
200 gives a suggestion of their appearance. 

The earth's shadow is similar in appearance to 
the moon's. The umbra is a cone whose base is 
about 8,000 miles in diameter, and whose length is 
about 868,000 miles. 

It is convenient to remember that the length of 
the earth's umbra is about equal to the diameter of 
the sun, but it is more to our present purpose to 
notice that it is nearly four times as long as the 
moon's umbra, and herein lies the reason for its 
darkening the face of the moon more often than the 
moon's shadow eclipses the earth. In Fig. 200 sun- 
light is supposed to come from the left-hand mar- 
gin of the page in lines deviating from parallel, as 
Fig. 199 represents, and lighting half of the earth 



300 



PHYSICS 



and moon. The umbra cast by each, with its proportional 
length, is shown*. The penumbra in each case may be im- 
agined. The moon is represented as approaching the part 
of its orbit where it will cast its shadow upon the earth. 
Persons upon the earth's surface will, where the shadow 
passes, notice a dark body apparently passing across the 
face of the sun. This phenomenon is called an eclipse of 
the sun. It requires about a month for the moon to re- 
volve around the earth ; hence in about half a month it 
will be approaching the earth's shadow, and when it passes 
through it, persons upon that part of the earth's surface 
turned toward the moon will notice a dark body apparently 
passing across the face of the moon. This phenomenon is 
called an eclipse of the moon. From this it would appear 
that there should be an eclipse of both sun and moon each 
month, but this is certainly not the case, an eclipse of the 
sun being very rare, and one of the moon occurring far 
from once a month. This is explained by the fact that the 
moon does not revolve in the same plane as that in which 
the earth's shadow lies, as will be seen by referring to Fig. 
201, which represents what we might suppose we would see 




Moon /Umbra 340,000 ^liles 

J 



Fig. 200. 



if we were to look down upon Fig. 200 from the direction 
of the top of the page. From this it would appear that an 
eclipse of neither sun nor moon might ever occur. 



But it 



RAYS OF LIGHT IN STRAIGHT LINES 301 

must be remembered that the earth accompanied by the 
moon is revolving around the sun in the plane in which 
ar, y, and z lie in Figs. 200 and 201, and there will be places 
in its orbit where eclipses may occur — eclipses of the moon 
far more frequently than eclipses of the sun, because the 
earth's shadow is so much larger than the moon's. It 



Fig. 201. 

must be true that whenever any place comes within the 
umbra, a total eclipse occurs for that place ; hence we see 
why partial eclipses are tolerably frequent, while total 
eclipses are very rare. It should be mentioned that the 
orbit of the earth is slightly elliptical, and therefore the 
sun is a little nearer at one time than another, and the 
umbra of both the earth and the moon must therefore be a 
little shorter at one time than another. For this cause the 
umbra of the moon is not long enough to reach the earth 
during a portion of each year. 

It may be interesting to note that two rays of light 
starting from opposite edges of the sun, and meeting at a 
point on the earth's surface, converge at the rate of 1 mile 
in 114; but if they extend from opposite edges of the sun 
to opposite edges of the earth, they converge at the rate of 
1 mile in 108. Of so little importance is the earth's diam- 
eter when considering the vast distances between the heav- 
enly bodies, that the earth may be looked upon as a mere 
point in space. A young child looking at the moon over 
his head thinks he may walk out from under it, and it is 
many years before he really appreciates that on account of 
the moon's great distance from the earth, it may appear to 
be overhead at the same moment to two persons situated 
many miles apart. 



302 PHYSICS 

282. Light through Small Apertures. — In Fig. 202, cd 
represents a very small hole, about one tenth of an inch, in 
a piece of cardboard an inch or two in front of a candle 
flame, and a screen is held a few inches behind it. An 
inverted image of the flame will appear upon the screen. 
The reason for the image being inverted and for its be- 
ing more or less indistinct will be seen from a study of 
the figure. Light from the tip of the flame a will fall 
upon the screen at a' and will cover an area somewhat 
larger than the hole c d. Likewise a point, b, at the base 
of the flame, will illuminate that portion of the screen 
marked V . The light which comes from the single point 
b not only spreads over an area considerably larger than 
the hole c d, but it is also overlapped by the light from 




Fig. 202. — Light through small apertures. 

neighboring points in the flame. Hence the image is 
more or less indistinct. When a pencil, or similar object, 
is passed downward between the flame and c d, the shadow 
of the pencil moves upward upon the screen, and vice versa ; 
also when the pencil is moved horizontally in a direction 
parallel to the screen its shadow makes the reverse move- 
ment. 

A Camera made from a Small Pasteboard Box. — A hole 
scarcely one tenth of an inch broad is made in the cover of 
a small pasteboard box and a window about two inches 
square is cut in the bottom of the box ; over this the thin- 
nest tissue paper is pasted. A candle flame is placed before 
the small hole about an inch and a half distant. An in- 



RAYS OF LIGHT IN STRAIGHT LINES 303 

verted image of the flame appears upon the tissue-paper 
screen. This is seen much more plainly when a dark 
cloth, such as photographers use, is thrown over the head 
to shut the outside light from the eyes and from the 
screeu. 

This box represents a camera, and although it has no 
lens it takes a very fair picture of a landscape when a 
sensitive plate, such as photographers use, is placed in the 
bottom of the box. This must be done in a dark room, 
and a cloth must be wrapped around the box to prevent 
light from getting in and spoiling the plate before one is 
ready to take the picture. In taking the picture the cloth 
is removed from the small hole — not from the rest of the 
box — for a brief interval and then replaced, and the plate 
is taken out of the box in a dark room and put into the 
developing solution which photographers use. Such a 
pasteboard box as the sensitive plates come in serves well 
for this kind of a camera. 

A Picture received through a Keyhole. — In the evening 
one may get an inverted picture through a keyhole by going 
into a dark room and holding a thin piece of paper a foot 
or two from the keyhole of the door, while some one holds 
a lighted lamp about the same distance from the other side 
of the keyhole. 



CHAPTEK XXVII 

REFLECTION OF LIGHT 

283. Laws of Reflection. — The angle which a ray of light 
makes with the perpendicular to a reflecting surface at the 
point where the ray strikes is known as the angle of inci- 
?, (i, Fig. 203). After reflection the ray makes a second 







% [_ /■ 




Fig. 


203 


Mirror 
— Law of reflection. 



angle with the perpendicular, known as the angle of reflec- 
tion, r. Two simple laws are found to hold in all cases of 
reflection : 

1. The angle of reflection is equal to the angle of inci- 
dence. 

2. The incident ray, the perpendicular, and the reflected 
ray are in the same plane. 

Heat rays are reflected in the same way. A billiard ball 
sent against the cushion tends to return according to the 
same law; other causes, however, operate to change the 
direction in this case. 

284. Images in Plane Mirrors. — If such a reflected ray 
enter the eye, it produces there an image of the point from 
which it has come, but the image will not seem to be in the 
304 



REFLECTION OF LIGHT 



305 




Fig. 204. — Location of image. 



direction of the incident ray, but will appear lack of the 
reflecting surface as far as the real object is in front of it, 
and in the direction of the reflected ray produced. Such 
an image has, of course, no real existence. All the images 
produced by plane mirrors 
are of this character. They 
are constructed as follows : 

Let MR (Fig. 204) be the 
surface of a plane mirror, and 
let a represent an object in 
front of it. We may locate 
the point where we imagine 
the image to be as follows : 
Consider any two rays pass- 
ing from a to the mirror as 
a c and a d. They will be 
reflected in obedience to the first law, the angle of reflec- 
tion, in both cases equaling the corresponding angle of in- 
cidence. Producing the reflected rays, they are found to 
meet at a', as far back of the mirror as a is in front of it. 

However complicated the object may be, its image is 
found in precisely the same way, practically by dropping 
perpendiculars from various points in an object to the mir- 
ror, and extending 
them to the rear as 
far as the actual 
points are to the 
front. Fig. 205 
shows how rays of 
light will pass from 
a and b, the two ex- 
tremities of an ob- 
ject, to a mirror, 
MR, and be reflect- 
ed from the mirror to the eye of the observer at e, the 
image of the object appearing at a' V. The image, while 
21 




Fig. 205. — Location of image. 



300 



PHYSICS 




resembling the object in every other particular, is re- 
versed. 

285. Concave Mirrors — Principal Focus and Conjugate 
Foci. — Let aob (Fig. 206) represent a concave mirror, and 

let rays of light, 8 a and Sb, 

, fall on its surface parallel to 

the principal axis, do. If d be 
\, % the center of curvature of the 

i— — ^ -~>d mirror, lines drawn from d to 

,**** any point on the surface of the 

mirror will be perpendicular at 

~ ^ that point. Hence any ray, 

8 a, will be reflected to a point 

Fig. 206.-Eeflecto by a con- ^ g() located that 8ad e q ualg 

Fad. All parallel rays will be 
approximately reflected to F, which is called the Principal 
Focus of the mirror. Conversely, all rays originating at F 
will be reflected parallel to the principal axis d o. 

Eays of sunlight may be considered parallel. They may 
be collected at F, which would thus be a center of great 
heat. This may be shown experimentally by turning a 
concave mirror toward the sun and finding F. 

Conjugate Foci. — A source of light must be infinitely 

distant to send parallel 

rays to the mirror. Let us 

consider a nearer source of 

* light, such as a candle at a 

(Fig. 207). The rays are (. J^^C;::^ ;^u 

divergent, and after reflec- 
tion will be gathered to 
some point, /, farther from 
the mirror than the prin- 
cipal focus is. Conversely, Fig. 207.— Conjugate foci, 
rays originating at /would, 

after reflection, be gathered at a. Points so related as a and 
/ are called Conjugate Foci, since they are interchangeable. 




REFLECTION OF LIGHT 



30' 



286. Enlarged Images formed in Concave Mirrors. — In 

Fig. 208, a b represents the curved mirror, d is the center 
of its curve, the eye is supposed to be at e, and m n is an 
object. A ray of light from m reaches the eye by being 
reflected at c so as to make the angle of incidence, m c d, 
equal to the angle of reflection, dee. And it appears that, 
of all the rays of light which pass out from m and fall upon 
the mirror, this is the 
only one which may 
reach the eye. One 
should convince him- 
self of this fact by 
drawing a series of dia- 
grams showing the 
course which various 
rays from m to the mir- 
ror will take upon being 
reflected according to 
the law. The image of 
the point m appears to 
be behind the mirror 
in the direction e c, but 
the distance of m' from 
e is determined by the 
imagination, which dif- 
fers with different peo- 
ple. In this book m! 
has been located so that 

t ig. 208. — Enlarged images. 

m' c shall be equal to 

m c, because this seemed to be as reasonable as any other 
conclusion, and it is a convenient measurement. In like 
manner the image of each of the points n, o, and p will 
appear behind the mirror at n\ o\ p', the extremities of 
lines e c'", and e e' and e c", extended so that c'" n', e o', 
and c" p' shall be equal to e'" n, c' o, and e" p respectively. 
The angles of incidence and reflection are in every case 




308 



PHYSICS 



equal to each other. The image appears curved and en- 
larged. It appears enlarged both because it seems to sub- 
tend a greater visual angle, and because it seems- to be 
farther distant than the object ; it appears curved for rea- 
sons which are given in section 290. 

287. How an Inverted Image is formed in a Concave 
Mirror. — In Fig. 209, m n represents a vertical line across 
the face, e the position of the eye, a b the mirror, d the 
center of the curve, c and c' the places upon the mirror 
where the rays of light from the points m and n respect- 
ively are reflected to the eye. Of all the rays of light 
which pass out from w, the one which meets the mirror at 
c is the only one which can be reflected to e, because it is 
the only one which can make the angle of incidence, m cd, 
equal to the angle of reflection, e c d. Hence the image of 
the point m will appear in the direction e c, and that of n 
in the direction e c'. The image m' n' will therefore repre- 
sent the object turned end for end or inverted, and the 
image appears to be located about as 
far behind the mirror as the object is 
in front of the mirror. It does not 
appear curved in this case. For a dis- 
cussion on this point see section 290. 

When the mirror is near the face 
an upright image is seen, which grows 
rapidly larger as the mirror is moved 
farther away. The image soon be- 
comes very indistinct, some parts ap- 
pearing double, and then an inverted 
image of large size appears, which 
grows smaller as the mirror continues 
to move farther away. 

The reason for this will appear to 
any one who will take the trouble to 
draw a series of diagrams after the plan of Fig. 209, in 
which the object m n shall be represented in various posi- 




m' 



Fig. 209.— Inverted 
images. 



REFLECTION OF LIGHT 



309 



tions, some of which shall be between the center d and the 
mirror. It will be found that direct images will be pro- 
duced in all cases where e is between d and the mirror, 
and that inverted images are produced when e is farther 
from the mirror than d is, and that the nearer e is to d the 
larger is the image. 

288. Diminished Images formed in a Convex Mirror. — 
Fig. 210 represents a case where the convex side of the 
mirror is turned toward the face. 

The image always appears direct, 
always smaller than the object, 
and grows smaller as it recedes 
from the mirror. The figure 
represents the relation of the 
image to the object for one sin- 
gle position. It will be found 
to be instructive to make a 
series of diagrams for various 
positions which the object may 
occupy. 

289. A Silver Spoon as a Concave and a Convex Mirror. — 
The bowl of a bright silver spoon gives images that are 
enlarged or diminished in some directions more than others 
— i. e., the image is not a symmetrical representation of the 
object, as it always is when a true spherical mirror is used. 
This is due to the fact that the bowl of the spoon has a 
curve of a smaller circle from side to side than from end to 
end. A little experimenting with a piece of bright tin by 
bending it more or less while observing one's face in it will 
reveal the fact that in the case of convex mirrors the image 
always grows smaller as the mirror becomes more convex ; 
but, in the case of concave mirrors, as long as the object is 
farther from the mirror than the center of the curve, the 
image grows smaller as the mirror becomes more concave; 
if, however, the object is situated between the mirror and 
the center of the curve, the image enlarges as the mirror 




Diminished images. 



310 PHYSICS 

becomes more concave. This latter condition is never real- 
ized when one observes his face in the bowl of a spoon. A 
series of drawings like those represented in Figs. 209 and 
210, in which the curve of the arc a b shall vary, will fur- 
nish an explanation of these phenomena. 

290. A Curved Image from a Straight Object. — The 
image of a straight object appears curved in either convex 
or concave mirrors only when the object is very near to the 
mirror. It would appear, referring to Fig. 208, that, under 
these conditions, the mind instinctively conceives m' o, o' c', 
p' c", and n' c'" to be respectively equal to m c, o c\p c", 
and n c"\ and that it is unable to recognize that relation- 
ship when the object is more remote from the mirror. 
This may be due to the fact that when the object is far 
from the mirror its image must be looked at very nearly in 
the plane of its curve, if it has one, and the eye fails to 
recognize the curve, just as it can not see the curve of a 
circle when looked at edgewise. 



CHAPTER XXVIII 

MISCELLANEOUS OBSERVATIONS ON REFLECTION 

291. How Daylight is diffused. — Every one knows that 
mirrors reflect light, but few, if any, appreciate what a 
tangled lot of reflected and re-reflected rays we are using 
continually. All things reflect light to a greater or less 
degree. 

It is easy to see that, although the direct sunlight is 
parallel and travels in straight lines, it scarcely travels far 
after it reaches the earth without meeting various objects 
which reflect it in all possible directions and into every 
nook and corner. 

292. Halos about Street Lights and the " Circle around 
the Moon." — A beam of sunlight passing into a dark room 
is made apparent by particles of dust which reflect the light 
to the eye. If one takes a piece of glass and breathes upon 
it to bedew it with moisture, and holds it* very near to the 
eye while looking through it at a candle flame, the flame 
will have the same appearance as the street lights do upon 
foggy nights. The small particles of moisture reflect light 
as the particles of dust do. These, distributed everywhere 
in the atmosphere, reflect the light of the moon at night, 
but only those occupying certain positions with reference 
to the observer can reflect light to his eye. This phenome- 
non may indicate the presence of much moisture in the air, 
but that does not always presage a storm. 

293. "The Sun drawing Water." — The phenomenon 
which some people call " the sun drawing water " is pro- 

311 



312 PHYSICS 

duced by particles of dust or moisture in the atmosphere 
reflecting sunlight and marking the path of sunbeams 
which pass out from behind a cloud. These sunbeams are 
frequently seen in the latter part of the afternoon shooting 
upward toward the zenith as well as downward toward the 
horizon. People who suppose they are streams of water 
can not take the trouble to consider the difficulties which 
might appear to be counter to such a supposition. 

294. Illumination of Clouds at Sunset. — Clouds, like the 
moon, catch the sunlight and reflect it to us after sunset. 
We see them best when the direct sunlight is shut off from 
our eyes by the horizon, but is still shining upon the clouds, 
just as we see the moon after the sun has gone out of our 
sight, but is still shining upon it. 

295. Moonlight and the Phases of the Moon. — We are 
wholly unable to see an object unless light comes from that 
particular object to the eye. The moon is visible only when 
the sun shines upon it, and only that portion of it is visible 
upon which the sun shines, excepting that the dark part 
of the new moon is slightly illuminated by light reflected 



eo 



FIRST 
QUARTER 



MOON 



Fig. 211. — Phases of the moon. 

upon it from the earth, and is somewhat visible by this 
light being reflected back again from the moon to our eyes. 
Fig. 211 is intended to explain the phases of the moon. 
Sunlight is supposed to come from the right-hand margin 
of the page in parallel lines and illuminate the right half 



MISCELLANEOUS OBSERVATIONS ON REFLECTION 313 

of m', m", and m'", which represent the moon in three posi- 
tions — in the western horizon, in the zenith, and in the 
eastern horizon. E represents the earth, the right half of 
which is also illuminated by sunlight ; a represents the posi- 
tion of an observer upon the earth. 

Suppose the observer looks at the moon when it is in 
the position m' ; the earth meanwhile is turning over in 
the direction indicated by the arrow, carrying the observer 
into the darkened portion where he no longer sees the 
direct sunlight. The sun appears to sink below the west- 
ern horizon, but the moon is still a little above the horizon, 
and he sees a little of the side of it which the sun is shining 
upon, and it appears crescent-shaped and is called the new 
moon. About a week later, at the same time in the day, 
when he looks for the moon he will find it overhead in a 
direction ninety degrees from that of the sun, and it will 
appear like a semicircle. It is then said to be in first 
quarter. In another week at sunset he will find the moon 
upon the eastern horizon showing a complete circle, when 
it is called full moon. These appearances of the moon are 
called phases of the moon. 

296. How the Dark Part of the New Moon is made Visi- 
ble. — If we could transfer ourselves from the earth to the 
new moon, we should be able to look back upon the earth 
as upon a full moon four times as broad as the moon itself 
ever appeared to us from the earth, and reflecting sixteen 
times as much light, because its apparent area would be 
sixteen times as great as that of a full moon. The earth, 
then, shines so brightly upon the darkened side of a new 
moon that it illuminates it sufficiently to make it visible 
from the earth when the atmosphere is very clear. Clouds 
in our atmosphere might interfere with the earth's giving 
so much light to the moon as stated above, and they inter- 
fere with our receiving the light reflected back again from 
the moon. Whenever, therefore, we see the dark portion 
of the moon we may remember that we are receiving into 



314 PHYSICS 

our eyes sunlight which has been first reflected from the 
earth to the moon and then back again from the moon to 
us. If we could visit the moon in " first quarter," the earth 
would appear to us as a larger moon in the " first quarter " ; 
and if we could visit the full moon, the earth would appear 
as a very large new moon. In neither of these cases does 
the earth reflect light enough to the moon to make its dark 
part visible to the earth. 

Venus at all times, as seen through a telescope, appears 
like a new moon. 

297. Why are Transparent Objects and Very Good Reflect- 
ors so nearly Invisible Themselves ? — It seems probable that 
if an object could be either perfectly transparent or a per- 
fect reflector it would be wholly invisible. When a bottle 
is entirely filled with very clear water it often appears 
empty. Window panes may be so clear that it is difficult 
to tell whether they are present or wanting. Air is invisi- 
ble because of its transparency. Moreover, a mirror is often 
well-nigh invisible itself because it is so perfect a reflector 
of light. Most substances reflect a part only of the light 
which falls upon them, and transmit or absorb the rest. A 
glass put over a picture often transmits too little light and 
reflects too much to serve well its purpose. The same is 
frequently true of a show window. It is particularly so the 
more obliquely one attempts to look through them. It is 
also a matter of familiar experience that, when one attempts 
to look through a window from the outside, the farther he 
is from the window the greater is the proportion of reflected 
light, and the nearer he is to the window the greater is the 
proportion of transmitted light. 

Objects which are nearly invisible, either because they 
are good reflectors or because they transmit light well, 
become readily visible if covered with dust or moisture or 
are scratched, or if in any way the surface is made rough, 
A bright tin reflector may be scoured with sand or scratched 
with a file so that it will no longer reflect an image. A 



MISCELLANEOUS OBSERVATIONS ON REFLECTION 315 

glass mirror might be treated in the same way. Trans- 
parent glass, if treated in this way, loses its transparency 
and becomes " ground glass." A quiet body of water which 
acts like a mirror ceases to do so when ruffled by a -breeze. 





Fig. 212. Fig. 213. 

The accompanying figures (212 and 213) present an 
explanation for this fact. 

298. Visibility of Print upon Glazed andUnglazed Paper — 
Drawings upon Rough and upon Highly Polished Surfaces. — 

AH objects have a somewhat ruffled surface, and it seems 
probable that they are themselves made visible, not by the 
light which they transmit or reflect from a smooth surface, 
but by the rays which they scatter. Thus, in Fig. 212, the 
rays of light which meet the eye at e from the various 
points of the arrow abed, being reflected in regular order, 
make the observer conscious of the arrow, but not of the 
mirror ; on the other hand, in the case represented in Fig. 
213, a jumble of rays from a great variety of objects is 
reflected to the eye, and the mind, not being able to form 
an image of any object beyond the mirror, traces the light 
only so far as the mirror itself, and is conscious of that 
alone. 

It is much easier to read from a rough page than a 
glossy one. Drawings and paintings show much better 
from rough than from highly polished surfaces. Polished 
blackboards would be of little use. Shading a picture with 
crayon is only a matter of diffusing the light which it will 
reflect. 



316 



PHYSICS 



299. Twilight. — Every one who is at all thoughtful 
concerning natural phenomena must sometimes ask the 
question, Why, after the sun has set, does light linger 
so long and darkness come so slowly? This period be- 
tween day and night we call tivttight. It occurs in the 
morning as well as in the evening. It lasts much longer 
in summer than in winter. We may properly consider 
one of the causes of twilight in this chapter ; it is reflec- 
tion. In Eig. 214, E represents the earth. Sunlight comes 
from the right-hand side. U U is the umbra, a a a is the 
atmosphere. The ratio of its depth to the diameter of the 
earth is greatly exaggerated, however. The arrow shows 
the direction in which the earth rotates. is the position 




Fig. 214.— Twilight. 



of an observer for whom the sun has set, and he is now in 
the region of twilight. Clouds and innumerable particles 
of moisture and dust floating in the atmosphere above still 
catch the sunlight and reflect it down upon him. In the 
morning he will enter another such region of twilight, rep- 
resented at the lower margin of the figure, before he receives 
the full light of the sun. 



CHAPTER XXIX 

REFRACTION OF LIGHT 

300. Refraction of Light defined and illustrated. — The 

fact that rays of light are bent in passing through various 
transparent substances is illustrated on every hand. This 
bending of rays of light is called refraction. It only requires 
that one should be fairly attentive to what he sees about 
him to become familiar with most of the phenomena of 
refraction. At the dinner- table one may see objects through 
his tumbler of water, not only apparently displaced, but 
also enlarged, distorted, and even inverted horizontally. 
The handle of a teaspoon in the tumbler of water may 
appear to be broken. A bubble or a crack in a window 
pane may make an object outside appear to be broken, dis- 
placed, or distorted. An inkstand, a paper-weight, a bev- 
eled mirror, or other household articles may give prismatic 
colors. 

When a beam of light passes obliquely from one medium 
to another of different density, as from air into water, or 
air into glass, it suffers refraction. The entire beam does 
not enter the second medium. A part of it is thrown off 
as a reflection. The part that enters the second medium is 
not all refracted. A portion of it is absorbed and appears 
as heat. The portion that is refracted is subject to definite 
laws, just as the reflected part is. 

Refraction may be conveniently studied by means of a 
glass vessel with parallel sides, on which a circle is painted 
(Fig. 215). The vessel is filled with liquid, say water, up to 

317 



318 



PHYSICS 



= 1.33. 



the horizontal diameter of the circle. A lamp is placed at 
L, so that its light will strike the water at the center of the 
circle. If the experiment is performed in a dark room, it 
will be plainly seen that where the light strikes the water 
its rays are bent toward the perpendicular. 

301. Index of Refraction.— The amount of refraction is 
measured in this way : a o and d o being made equal, the 
distance of each of these points 
from the perpendicular is meas- 
ured and compared : 
ab_ 4 
dc~ 3 
This value is called the index of 
refraction. It is found to be 
constant for any two given me- 
dia, however much the obliquity 
of the ray of light may change 
— i. e., so long as the two media 
remain air and water, we may 
change the direction of the ray 
ao, and consequently the value of a b, never so much, dc 
will likewise change so as to be three fourths of a b. 

The index of refraction varies with different media. 
For light passing from air into ether it is 1.36 ; into alco- 
hol, 1.37 ; into turpentine, 1.47 ; into crown glass, 1.53 ; 
into flint glass, 1.63 ; into carbon bisulphide, 1.67 ; into 
diamond, 2.75. 

It is manifest from this that optical density is not the 
same as ordinary density ; for, although ether, alcohol, and 
turpentine are all lighter than water, they have a larger 
index of refraction. This is illustrated in Fig. 219. The 
following laws are found to hold : 

1. The incident ray, the perpendicular, and the refracted 
ray are in the same plane. 

2. When light passes from an optically rarer into a 
denser medium obliquely to the surface, which is between 




Fig. 215.— Eefraction. 



REFRACTION OF LIGHT 319 

the two media, it is bent toward the perpendicular to that 
surface ; or, conversely, if it passes from a denser into a 
rarer medium, it is bent away from the perpendicular. 

3. The index of refraction is always a constant value for 
any two given media, however much the obliquity of the 
ray may change. 

302. Cause of Refraction. — These facts are purely experi- 
mental, and therefore quite independent of any theory. 
But we have now to inquire why the ray is bent a definite 
amount if oblique, and is not bent if perpendicular. Sup- 
pose a beam of light with a wave front, IV (Fig. 216), to 
strike obliquely against the surface of water, s s. It has 
been found by experiment that light travels one third again 
as fast in air as in water. Consequently the whole wave is 
retarded in the water. But all portions of the wave front 
do not enter the water at the same time. When I reaches 
ss, V is still some distance away. If, now, I traveled as fast 
as V, the beam would pass into the second medium without 
any bending, as indicated in the dotted lines. But this is 
not the case ; while V passes 
to ss, I can only go three 
fourths as far — that is, to h 
— and hence the wave front 
swings around to It h\ and 
the beam itself, which must 
always be perpendicular to the 
wave front, takes the new 
direction shown, bent toward /' M¥§i 

the common perpendicular, /r f < -',, ),// 

hli'. When the beam is per- ' / 

pendicular to s s, the wave fig. 216.— Refraction. 

front IV, is equally retarded 

along its entire length, and consequently there is no change 

of direction. 

303. Value of the Index. — The numerical value of the 
Index of Refraction is always the ratio of the velocity of 




320 



PHYSICS 



light in the first medium to the velocity in the second. 
When, therefore, light passes into a medium of greater 
density, the index is always greater than one, and the ray 
is bent toward the common perpendicular. When light 
passes into a medium of less density, the index is always 
less than one, and the ray is bent away from the common 
perpendicular. 

When the direction of a beam is reversed, the second 
becomes the reciprocal of the first. Thus, the index, when 
light passes from air into water, is f ; but when light passes 
from water into air, the index is f . 

304. The Critical Angle. — It follows from all this that a 
ray of light can always pass from a rare into a dense medium, 




Fig. 217.— Critical angle. 

because it is bent toward the common perpendicular ; but 
the ray can not always pass from a dense into a rare 
medium, for if the ray should be bent away from the com- 
mon perpendicular more than 90° it would fail altogether 
to emerge from the denser medium. No ray of light can 
pass from water into air if it makes a greater angle with 
the perpendicular than 48° 35'. 



REFRACTION OP LIGHT 321 

Referring to Fig. 217, let A B represent the surface of 
water. A ray of light starting from a will be bent so as to 
reach a', likewise those which start from b and c will reach 
V and d respectively, but one which starts from d would be 
bent so as to pass along the surface through B, and one 
which starts from i would be bent so as to return beneath 
the surface of the water to i'. 

305. Total Reflection. — We may well be interested to 
inquire what becomes of rays which make greater incident 
angles than the critical angle, and which consequently can 
not emerge. 

They are reflected, and since the reflection is complete, 
it is called total reflection. Could we stand at the bottom of 
a pool of clear water and look upward, we should see objects 
on the surface of the water within a cone which had our 
eye for its apex, and whose elements made an angle of 48° 
35' with its axis. Beyond the circular base of this cone we 
should see a perfect mirror, which would reflect objects 
lying on the bottom of the pool. The same effect on a 
small scale may be seen when we look at the underside of 
the surface of water in a clear tumbler, provided the angle 
of vision be greater than the critical angle. The surface 
appears like a burnished mirror. A silver spoon or a bright 
coin will give a brilliant image. For the same reason, water 
in a test-tube seems covered with a film of silver when 
looked at from below. 

306. Applications. — Eefraction is the source of many illu- 
sions. Bent rays of light make objects appear where they 
are not. The sun, moon, and stars, when near the horizon, 
are elevated about half a degree by the refraction of the 
earth's atmosphere. This is equal to the apparent diam- 
eters of the sun and moon. Sticks and other objects partly 
immersed in water appear bent at the surface (see Fig. 218). 
Clear water appears less deep than it really is. The hot air 
over the surface of a desert bends the rays of light and 
produces the mirage, the appearance of reflection in water. 

22 



322 



PHYSICS 



Precious stones owe their brilliancy to high refractive 
power, and consequently to total reflections from the facets 
on the other side. The critical angle for the diamond is 
23° 53'. All the light that passes into the diamond, and 
strikes any of the facets at angles greater than this, suffers 






^^ 


^=^ 




5^ 


^^ 


INDEX OF 


















TURPENTINE 










-—1.47 


















CARBON BISULPHIDE 










1.67 




Fig 


. 219 







Fig. 218.— Eefraction. 



total reflection within the stone, and finally emerges in pen- 
cils of light, which produce the magnificent fire and sparkle 
of the gem. Many of the rays of light are so refracted as 
to produce prismatic colors. The diamond owes all its 
brilliancy to the cutting, for in its natural state it is dull. 

Our heaviest flint glass has a critical angle of 35° 37'. 
Artificial diamonds made of this material must, therefore, 
have much less brilliancy than the real stone. If we could 
make a glass as transparent as the diamond, and having an 
equally high refractive index, we should have an equally 
brilliant gem. 

Refraction of light enables us to see colorless and trans- 
parent fluids. Fig. 219 represents a bottle which contains 
three colorless and transparent liquids. They remain sepa- 
rate from one another as oil and water do. Carbon bisul- 
phide is at the bottom, upon this floats the water, and upon 
the water floats the turpentine. A straight line is drawn 
vertically upon the back face of the bottle, and this, as seen 
through the liquid obliquely, appears as a broken line, by 
reason of the differing powers of refraction of the liquids. 



REFRACTION OF LIGHT 



323 



The fact that we may distinguish between these various 
liquids is due to the variation in their refracting power. 
Air refracts light, and cold air more than warm air. This 
is the reason why we can see hot air rising above a stove. 
Small currents of warm air pass up. through the cold air, 
and rays of light coming from objects seen through these 
currents of air are made to quiver by reason of rapid 
changes in their refraction. Something similar appears 
when one of the liquids mentioned above is poured in a 
small stream into another in the bottle. It is well shown 
by pouring glycerin into water. 

Refraction enables us to see the sun two minutes after 
it has set and two minutes before it rises, hence it has the 
effect of lengthening the day four minutes. Reflection, by 
producing twilight, lengthens the day several hours. We 
may see the sun ten minutes after it has set, on account of 
both refraction and the velocity of light, but on the same 
account we do not see it until six minutes after it has risen. 





Fig. 220. 



Fig. 221. 



A body of clear water, which when calm may reveal 
objects at great depths, will not do so when the surface is 



324 



PHYSICS 




Fig. 222. — Refraction by a prism. 



disturbed by a breeze. This is due to refraction, as will be 
seen from Figs. 220 and 221. In Fig. 220 each point in 
the object abed under water sends its light in regular 
order to the eye, e, held above the water, but in Fig. 221 
these rays are so bent as to give a confused image. 

307. Refraction in Prisms. — The path of a ray of light in 
passing through a prism is illustrated in Fig. 222. Suppose 

BE to be an incident ray 
upon the face of a glass 
prism. After refraction the 
ray will take the direction 
EI, being bent toward the 
perpendicular at E, and will 
suffer a second refraction 
at /. Here the ray is pass- 
ing into a less dense me- 
dium, and must consequent- 
ly be bent away from the perpendicular, and must take 
some such direction as IS. From the nature of the case, 
the ray is always bent toward the base of the prism — that 
is, toward the thicker part. 

308. Enlarged Images produced by Refraction. — A cross- 
section of a prism is represented in Fig. 223 ; m n repre- 
sents an object, and e the 
position of the eye. The 
object appears to be en- 
larged to the size of m' n\ 
which may be measured 
and perhaps found to be 
half as large again. The 
ratio of the size of the image to the size of the object 
is expressed thus : 

m! n' 15 mm. . „ 

= zr^ = 1.5. 

m n 10 mm. 

309. Different Kinds of Lenses and the Way they refract 
Light. — If the prism mentioned above were slightly modi- 




Fig. 223 



REFRACTION OF LIGHT 



325 



fied in shape so that its cross-section would look like Fig. 
224, b, we should call it a lens, and, since one of its surfaces 




b c d e 

Fig. 224.— Typical lenses. 



is plane, while the other is convex, it would be called a 
plano-convex lens ; if the plane surface were made convex 
also, it would be called a double-convex lens (a) ; if one sur- 
face were plane while the other were concave, as repre- 
sented at e, it would be a plano-concave lens ; and if both 
surfaces were concave, it would be called a double-concave 
lens (d). 

After what has been said, it is a simple matter to under- 
stand how rays of light will be bent in passing through 
these lenses. The principle to be borne in mind is that 
when a ray passes from air into glass it is bent toward the 
perpendicular, and when it passes from glass into air it is 
bent away from the perpendicular. It is evident that the 
lens represented at e, for example, makes the image appear 
smaller than the object, and that the lens at a has the 
greatest magnifying power. 

310. Inverted Images produced by Refraction. — In Fig. 
225, a b represents a lens, m n represents an object, and 
n a e and m b e are lines of light which pass from the ex- 
tremities of the object through the lens to the eye, which 
is supposed to be situated at e. The image m' n' appears 
to be inverted. The reason for this is not hard to find. 
Rays of light pass out from the point m in all directions. 
One ray takes the direction of the line m b e. The mind 



326 



PHYSICS 



conceives that it sees m in the straight line e h at m'. For 
the same reason the image of n appears at n! — i. e., the image 
of the arrow appears to point in the opposite direction from 
the way the arrow itself points. JSTone of the rays of light 
which start from the points m and n and fall upon the lens 



.n'. 




n 

~ -- hn' 
Fig. 225. — Enlarged and inverted image. 

can reach the eye except those which pass through i and «, 
as represented ; all others will be bent, according to the law 
of refraction, so as to pass one side or the other of the eye. 

311. The Path of Rays of Light exhibited by Crayon- 
dust — Measuring the Focal Distance of a Lens. — When the 
lens is held in sunlight and plenty of dust is made to 
float in the air around it, by beating blackboard erasers or 
dusty clothing near it, the rays of light are easily traced 
by means of these reflecting particles, and they are seen to 
meet and cross, forming two cones of light as represented 
in Fig. 226. The points where the apices of the cones 
meet is the principal focus, and its distance from the lens 
may be measured. 

These cones of light may be traced by using a screen. 
When the screen is brought against the face of the lens, the 
circle of light upon it is about the size of the lens. If the 




Fig. 226.— Principal focus. 



screen is placed halfway between the lens and the focus, 
the circle of light has about half the diameter of the lens ; 



REFRACTION OF LIGHT 327 

its area is therefore one quarter as great as in the first posi- 
tion, and the intensity of its light four times as great. 
When it is placed one quarter of the distance from the 
focus to the lens its circle of light is one quarter as broad 
and its area one sixteenth as great and the intensity of its 
light sixteen times as great as at the first position. At the 
focus it is a point of light of dazzling brightness, the heat 
of which is sufficient to burn a hole in paper when the 
experiment is tried in the brightest sunlight. The focal 
distance can be readily measured by placing the screen 
where the cross-section of the cone of light is nearest to a 
point and measuring the distance from the lens to the 
screen. 

312. Pictures formed at the Focus of a Lens. — When a 
lens is held before a screen at its focal distance, an inverted 
picture of distant objects is formed upon the screen. The 
objects in this case are so far away that rays of light from 
them are nearly parallel. When objects are brought nearer 
to the lens the screen must be moved farther away from 
the lens in order to receive the picture. A candle flame 
is a good object to experiment with, because it furnishes 
brighter rays of light than are reflected from objects in 
general. When the screen is placed so that a picture of 
the candle is formed upon it by the lens, the candle and 
screen occupy the positions of one pair of conjugate foci. 
If either one of these is brought nearer to the lens, it is 
found necessary to remove the other farther away, and 
vice versa. When a photographer takes a picture of a 
person sitting very near his instrument, he draws out the 
camera so as to move the plate which is to receive the 
picture farther away from the lens ; and when the person 
sits farther from the instrument, the operator moves the 
plate nearer to the lens by contracting his camera. 

313. To illustrate how a Lens forms a Picture. — It may 
be easy to see how a lens magnifies and inverts, but why 
should it form a picture at all ? 



328 PHYSICS 

If an object were placed before a screen without a lens 
between them, light would be reflected from every point 
on the object to every point on the screen, so that each 
point on the screen would receive an equal amount of 
light from each and all points of the object. In order to 
have a picture formed, each point of the object must send 
its light to one, and only one, point on the screen. This is 
brought about by the lens, as will be seen by reference to 
Fig. 227. All the rays of light which pass out from the 




Fig. 227.— Conjugate foci. 

point m and fall upon the lens are collected at the point 
m'. This is one pair of conjugate foci. In the same way 
all the rays which pass from n. to the lens are collected at 
n\ and these form another pair of conjugate foci. But 
when the screen is placed in focus for the light from m 
and n it is found to be out of focus for light from the 
points o and p, whose conjugate foci are found to be 
farther away from the lens than m' and n' are, because 
the points o and p are nearer the lens than m and n are. 
This consideration is important only when the object is 
near to the lens, for only then would the difference be- 
tween the distance of m and o from the lens be appreci- 
able. If, however, a photographer should attempt to take 
a picture of a group of persons formed in a straight line 
having his camera near the group, the individuals at the 
extremities of the group could not be in focus at the same 
time with those in the center. 

314. Material of Lenses.— The lenses used for optical 
purposes are made of flint glass. This is a double silicate 
of potash and lead. The lead makes the glass much more 



REFRACTION OF LIGHT 329 

dense, and gives it, consequently, a greater refractive index. 
For the same reason flint glass is used for the cut glass of 
tableware and toilet articles. Their cut facets have a very 
brilliant effect on account of refraction. 

315. Familiar Illustrations of Lenses. — Very many objects 
act as lenses. "When the eye is held near to a drop of 
water upon a window pane, an inverted picture of the out- 
side world is seen. If the sun is shining through it, a 
piece of paper held near it will show that the rays are made 
to converge to a point. Fish globes, and the globes used in 
drug-store windows, give magnified and inverted pictures. 
The neck of a small bottle magnifies so that if the bottle is 
filled to the neck with water containing microscopic objects, 
many of them may be seen. The animals which are usu- 
ally found in vinegar may be easily seen if the vinegar 
cruse is filled to the neck. 

316. The Simple Microscope. — A microscope is an instru- 
ment for enabling us to see very small objects by producing 
magnified images of them. The simple microscope is usu- 
ally a double-convex lens, and in use is so placed that the 
object to be viewed is back of the lens at a distance less 
than the focal length. Under these conditions we have a 
magnified and erect image. The construction of the image 
is of course purely imaginary. It has no real existence. 
But the imagination has the power of constructing such an 



Fro. 228. — Simple microscope. 

image, just as it has the power of constructing images back 
of a looking-glass. The rays that come from the object 
are bent by the lens, as shown in Fig. 228, and enter the 



330 PHYSICS 

eye at a wider angle than the direct rays would. This 
angle, known as the visual angle, determines the apparent 
size of objects. The simple microscope increases this angle, 
and consequently makes the object seem larger. 

317. Compound Microscope. — In its simplest form .the 
compound microscope consists of two lenses, the objective 
cd, and the eyepieces ab (Fig. 229). The two are mounted 




Fig. 229.— Compound microscope. 

in a tube on a suitable stand. In this way we have a 
double magnification, and the power of a compound micro- 
scope is equal to the product of the magnifying powers 
of the objective and the eyepiece. The image is inverted. 

In practice the compound microscope is very compli- 
cated in its construction. Both eyepiece and objective are 
themselves compound. In addition there are various ac- 
cessories for biological, mineralogical, and technical work 
that make the instrument quite an elaborate piece of mech- 
anism. 

318. The Telescope is an instrument for viewing objects 
from afar. There are two classes — the reflecting and the 
refracting. The latter are of the greater importance, but 
the former have played a historic part in astronomy, and 
are still doing good service in both England and France. 
The refracting telescope is, in its elements, very similar to 
the compound microscope. It consists of an objective and 
eyepiece. 

In astronomical telescopes it is desirable that the objec- 
tive should be as large as possible in order to include much 
light. The mechanical difficulties in the way of producing 



REFRACTION OF LIGHT 331 

large refractors are very great, but they have been success- 
fully overcome. The construction of such an instrument 
involves the combined skill of several nations. The glass 
is usually cast in France. The largest lenses, so far, have 
been ground by the Clark Brothers, in Cambridge, Mass. 
The mountings and requisite machinery are made where 
most convenient. The largest lens yet made is the giant 
objective of the University of Chicago, and is located at 
Lake Geneva, Wis. It is 40 inches in diameter. Next to 
this comes that of the Lick Observatory, in California — 91 
centimetres, or 35.82 inches, in diameter. The objective at 
the Imperial Eussian Observatory at Pulkowa, also made by 
the Clarks, is 76 centimetres, or 29.92 inches, in diameter. 

319. The Human Eye. — Most wonderful of all optical 
instruments is the human eye, and also the most imper- 
fect. Looking at the eye, what we see first is the trans- 
parent, bulging cornea, which is a modification of the outer 
coat of the whole eyeball, 
" the white of the eye," or 
the sclerotic coat (Fig. 
230). 

Immediately back of 
the cornea there is a cav- 
ity filled with a liquid 
known as the aqueous hu- 
mor. Back of this cavity 
there is a muscular screen, 

the iris, Which is annular FlG 230 ._SectioB of the human eye. 

in form, and gives color to 

the eye. The opening in the iris is known as the pupil. 
Under the influence of strong light the iris contracts, and 
the pupil becomes very small, so as to shut out as much 
light as necessary. In the dark, or in subdued light, the 
muscles relax and the pupils become larger. Directly back 
of the iris is the crystalline lens. It is transparent, and 
tough and elastic. The interior of the eyeball is filled with 




332 PHYSICS 

a jellylike substance, the vitreous humor. The innermost 
lining of the eyeball is the retina, formed by an extension 
of the optic nerve leading directly to the brain. Between 
the retina and the sclerotic coat is a black pigment, the 
choroid coat. 

In its operation the eye is quite similar to a photo- 
graphic camera. The crystalline lens is double convex, 
and forms an inverted image on the retina. The retina 
may be compared to the sensitive plate of the photographic 
camera, and the pupil, or opening in the iris, which serves 
to admit more or less light, may be compared to the dia- 
phragms, or stops, used for the same purpose in the cam- 
era. So far it is very simple and well understood. But 
our explanation ends here. As a physical fact, the image 
on the retina means simply light-waves of varying wave 
length and intensity, and these have varying effects upon 
the nerves of the retina. All these complex impulses pass by 
means of the optic nerve to the brain, and it is in the brain 
that we see. But how these nerve impulses get translated 
into a mental impression we are quite at a loss to explain. 
We have said that the human eye is one of the most 
imperfect of optical instruments. Few persons have per- 
fect eyes. 

Cataract is caused by the crystalline lens becoming 
opaque, and therefore ceasing to transmit distinct rays. 
Operations are sometimes successfully carried out by 
which the lens is removed altogether and sight restored, 
the humors in this case acting as the sole refracting me- 
dium. 

The common defects of vision, such as short- and long- 
sightedness and astigmatism, result from structural de- 
fects. Clear vision requires that a distinct image shall be 
formed on the retina. As the object, the crystalline lens, 
and the retina are fixed in position, the focusing can only 
be brought about by a change in the curvature of the lens. 
This is a matter of muscular contraction, and in normal 



REFRACTION OF LIGHT 



333 



eyes is done so quickly and unconsciously that we pass 
from the contemplation of distant to near objects, and vice 
versa, without the least difficulty. Xear-sightedness results 
from too great curvature of the lens, so that it forms 




Double-concave glass for near-sightedness. 



images in front of the retina. It is remedied by the use 
of glasses which cause rays of light to diverge (Fig. 231). 
Far-sightedness, on the contrary, results from too little 
curvature of the lens, so that images form back of the ret- 
ina. It must be remedied by glasses which cause rays of 
light to converge (Fig. 232). It is a universal defect of old 
age. Astigmatism means an irregular curvature of the 
cornea, by which the eye is never in focus for all objects 
in the field of vision, even at the same distance. It is 
remedied by special lenses combining spherical and cylindri- 




Fig. 232. — Double-convex glass for far-sightedness. 

cal surfaces. Few people have eyes that are perfectly adapt- 
ed for parallel vision. The muscular eifect necessary to 
bring them to parallel is a most frequent cause of headaches. 
320. The Spectrum. — We have seen that the index of 
refraction is in reality the ratio of the velocity of light in 
the first medium to the velocity in the second medium, and 
we have assumed that we had to deal with homogeneous 



334 



PHYSICS 



rays — that is, rays of uniform wave length. But white light 
is heterogeneous, consisting of wave lengths varying from 
.0004 millimetres in the violet, to .0007 millimetres in the 
red. These different rays are found to have different in- 
dices of refraction, and to suffer unequal bending on pass- 
ing into a second medium. In consequence, the various 
colored rays which, taken together, make a beam of white 
light, on passing through a prism are separated, so that the 
violet rays are on one side and the red rays on the other. 
If they be allowed to fall on a screen, we have the fine suc- 
cession of rainbow c61ors known as the spectrum (Fig. 233). 




Fig. 233.— The spectrum. 

Newton, in 1676, was the first to explain the matter. He 
distinguished seven primary colors, and named them violet, 
indigo, blue, green, yellow, orange, and red. It will be 
noticed, in looking at the spectrum on the screen, that the 
violet has been turned out of its path the most, and the 
red the least. The shorter violet waves are more retarded 
than the longer red waves in passing through the glass. 

A single prism will give a spectrum, but the effect will 
be magnified by combining a succession of prisms, and so 
increasing the total dispersive power. The train of prisms 
may be arranged in a circle, so that the beam of light con- 
stantly changes its direction and constantly widens (Fig. 
234). On the other hand, prisms may be combined in pairs, 
so as to neutralize one another (Fig. 235). 



REFRACTION OF LIGHT 



335 



There seems to be no limit to the possible length of 
ether waves. To produce any effect upon us, however, 
they must fall within 
very well-defined limits. 
The longest ether waves 
apparently have no ef- 
fect. As' they shorten 
they manifest them- 
selves as heat; as they 
grow still shorter they 
become visible as light, 
then as a source of chem- 
ical activity, and finally 
they again pass beyond 
the range of our sensa- 
tions. We perceive only 
a small part of the possi- 
ble waves. 

Color. — We should ex- 
pect these varying lengths of wave to affect us differently, 
just as the different pitch in musical notes, which is due 
to difference in length of air waves, and such, indeed, is 
the case. Color is the name given to this difference of 




Fig. 234. — A train of prisms. 




Fig. 235. — A pair of prisms. 

sensation, and depends wholly upon wave length. Ordi- 
nary sunlight contains waves of all lengths within the range 



330 PHYSICS 

of vision and is distinguished as white light. The range 
of vision lies between .0007 millimetres in the red and .0004 
millimetres in the violet. The following table shows the 
wave length corresponding to the different colors : 

Wave Length. Wave Length. 



Red 0007 ram. 

Orange 0006 mm. 

Yellow 00058 mm. 



Green : 00053 mm. 

Blue 00047 mm. 

Violet .0004 mm. 



321. The Invisible Spectrum. — At both ends of the spec- 
trum we have a dark region, quite invisible to the eye, but 
manifesting itself by its effects. Beyond the visible red 
we have a region of dark heat rays, which manifest them- 
selves if a delicate thermometer, such as a thermopile (see 
271), be placed in their path. We call this the heat end 
of the spectrum, and the colors at that end are sometimes 
referred to as warm colors. Beyond the visible violet we 
have another dark region, that of the so-called actinic rays, 
which have the power of bringing about chemical reactions, 
such as decomposing the sensitive silver salts used on photo- 
graphic paper, and of making certain fluorescent substances 
— such as fluor spar, quinine, and platino-cyanide of barium 
— visible in the dark. 

The invisible spectrum has a far greater range than the 
visible. In musical terms we might say that the visible 
spectrum covers about one octave. The heat spectrum 
extends for five octaves below the red, and the actinic or 
chemical spectrum for two octaves above the violet. 

We can easily imagine that the world would appear very 
different if our eyes were different in their power to per- 
ceive ether waves. 

322. Complementary Colors. — To produce white light it 
is not necessary to have waves of all lengths present. It 
is found, indeed, that two colors, if properly chosen, will 
suffice. As these extinguish each other, they are called 
complementary colors. Thus, red and greenish-blue, orange 



KEFRACTIOX OF LIGHT 337 

and Prussian blue, yellow and ultramarine, green-yelloAV 
and purple produce white light when taken in pairs. 
There appear to be three primary color sensations— red, 
green (slightly yellowish), and violet (bluish) — and when 
these are all excited at the same moment, the result is the 
sensation of white. Xo two of these primary colors can be 
complementary, for the third sensation would be lacking. 
But any one of the three is the complementary color of the 
result of the other two. Taking the pairs of colors men- 
tioned above, this principle will be found to apply. Thus, 
greenish-blue contains both green and violet, and is there- 
fore complementary to red ; purple, containing both red 
and violet, is complementary to green-yellow, etc. 

The phenomena of color are very fascinating and almost 
unending. In reality no objects are, properly speaking, 
colored. The sky is not blue, the grass is not green, the 
rose is not red. They appear so to us because of their 
effect on white light. The color ascribed to them is the 
color they reject. A bit of red glass is one that absorbs 
the complementary color, greenish-blue, and allows the red 
light to pass through, or else reflect it to us. If such a 
piece of glass be put into the fire, the red color remains 
so long as the glass is cooler than the fire — that is, so 
long as it is absorbing green. The color disappears when 
the glass has the same temperature as the source of heat 
back of it, for then the radiation emitted and absorbed just 
balance each other. If the glass be the hotter, it appears 
blue-green, for it is emitting more radiation than it is ab- 
sorbing. In general, we may say that substances emit radia- 
tions of the same wave length that they absorb. 

The Color Wheel — The blending of several colors into 
one impression may be capitally shown by means of a rotat- 
ing wheel or color-whirler (Fig. 236). Disks of colored 
cardboard may be attached and made to rotate with the 
wheel. Thus a disk having alternate sectors of black and 
white, when rotating appear a uniform gray. If the white 
23 



338 



PHYSICS 



sectors are larger, it will be a light gray ; if smaller, a dark 
gray. So red and blue produce purple. Complementary 
colors produce white. A disk having all the colors of the 
spectrum, properly proportioned, will produce white. The 
various pairs of colors opposite to one another in the circle 
(Fig. 236) are complementary and will produce white when 
confused together by rapid motion. 

Sunlight, according to Professor Rood, contains in 1,000 
parts the following ingredients : 

Green and blue-green. . 134 parts. 

Prussian blue 32 " 

Blue 40 " 



Red 54 parts. 

Orange-red 140 " 

Orange 80 " 

Orange-yellow 114 " 

Yellow 54 " 

Green-yellow 206 " 

Yellow-green 121 " 



Ultramarine and 

violet 

Violet 



blue- 



20 
5 



As the pigments used in coloring the pasteboard upon 
the color wheel are impure colors, one must not be disap- 
pointed if the impressions are somewhat muddy. They 
are, however, enough to the point to 
illustrate the truth of what has been 
said. The art of color mixing in 
painting is far from being the sim- 
ple matter it might at first seem, 
chiefly because of the tendency to 
chemical change which most pig- 
ments have. 

In modern picture windows, 

which in the hands of Tiffany and 

La Farge have become genuine 

works of art, the effects are often produced by doubling 

or even tripling the glass. Eobes of royal purple are thus 

obtained by separate thicknesses of blue and ruby glass. 

323. Fluorescence and Phosphorescence. — It is very plain 
that if by any operation we could change wave length of 
radiations, we should change their character. Retarding 




Fig. 



Green 

236. — Complementary- 
colors. 



REFRACTION OF LIGHT 339 

rapidity of vibrations and increasing the wave lengths 
might change chemical rays to light rays and light rays 
to heat rays, or change light rays of one kind into those 
of another kind. Quite a number of substances possess 
this power. Sulphate or quinine solution in the ultra- 
violet emits a pale-blue light; uranium glass gives a 
brilliant green ; fluorescein gives a beautiful green. The 
common mineral fluorite, CaF 2 , has the same power, and 
hence the name fluorescence has been given to the phe- 
nomenon. The platino-cyanide of barium is even more 
powerful. Its ordinary color is a dull yellow, but in the 
ultraviolet it gives a magnificent yellowish-green light. 

Phosphorescence, the power which certain substances 
have of emitting light in the dark after due exposure to 
strong light, is a similar property, but more persistent in 
character. The so-called " luminous paints," made usually 
of sulphide of barium, BaS, have this property, and serve 
to call our attention to the house number, the match box, 
and other articles usually sought for in the dark. 

But of far greater importance than even these beautiful 
phenomena is the change of wave length which takes place 
by the absorption and radiation again which occur in all 
forms of matter, since upon these depend very largely the 
habitability of the globe itself. The light radiations from 
the sun are thus changed by the earth into waves perhaps 
twenty times as long as the longest waves that are visible. 
Our hot-beds are constructed upon this principle. The 
light-waves pass through the glass freely, but when they 
appear as heat waves they are imprisoned. 

324. Temperature and Color.— The radiations given off 
from a slightly heated body are invisible. As the tempera- 
ture rises, the vibration frequency of the radiations appears 
to rise with it. If a platinum wire be gradually heated, by 
passing an electric current through it, a spectral gray color 
is emitted at about 400° C, and the wire appears as a dark- 
red line at 525°. As the temperature continues to rise, 



3i0 



PHYSICS 



waves of shorter and shorter lengths are constantly added, 
and the wire appears orange, then yellow, and finally in- 
tensely white. We are unable to perceive the colors toward 
the violet end of the spectrum because they are masked by 
the longer wave lengths already present. But the colors 
green, blue, and violet become visible if the longer wave 
lengths are filtered off by suitable glass. 

325. Ro'ntgen Rays. — In the year 1895, Professor W. C. 
Eontgen, of the University of Wiirzburg, announced his 
discovery of a new kind of radiation, which he modestly 
called X-rays, but which are more frequently designated by 
the name of their discoverer. The rays themselves are in- 
visible, but when allowed 
to fall upon certain phos- 
phorescent material, such 
as barium platino-cyanide 
or calcium tungstate, they 
cause it to emit rays of 
such length as to affect the 
eye. They also have the 
power to effect chemical 
changes in a photographic 
plate. All bodies are trans- 
parent to these rays, but 
in varying degrees. If, for 
example, we lay a hand 
upon the holder contain- 
ing a photographic plate, 
and let the Eontgen rays 
fall upon the hand, and 
then develop the plate, we 
find that the rays passed 
through the flesh of the 
hand more readily than through the bones, and through 
the bones more readily than through the metal finger ring, 
as shown by the varying degree to which chemical change 




Fig. 237.- 



-Photograph by Eontgen 
rays. 



REFRACTION OF LIGHT 



341 



was effected in the plate underneath these different parts 
of the hand (Fig. 237). Thus surgeons may locate a for- 
eign body, such as a bullet, in the flesh without probing 
for it ; and thus, too, they may locate abnormal growths, 
such as internal tumors, etc. 




Fig. 238. — Apparatus for Eontgen rays. 



The Eontgen rays are produced at the point where 
kathode rays, • which have been discharged into a high 
vacuum, strike upon a platinum screen or the walls of the 
vessel in which the discharge takes place. In order to 
obtain the necessary voltage to drive the electric current 
through the high vacuum, an induction coil may be used. 
Fig. 238 shows the vacuum tube, the induction coil, and 
the fluoroscope, into which the observer looks while hold- 



342 PHYSICS 

ing it turned toward the vacuum tube. The larger end of 
the fluoroscope has a screen coated with calcium tungstate or 
barium platino-cyanide, which fluoresces when the Ront- 
gen rays fall upon it. 

326. Herz Waves. — When a discharge takes place be- 
tween the knobs of an electrical machine (Fig. 137), or an 
induction coil (Fig. 186), in addition to the light rays 
which emanate from the spark, invisible rays pass out in 
every direction which have wave lengths of several metres. 
These are sometimes called Herz waves, because of the re- 
searches in that field made by a German physicist, Heinrich 
Herz (1857-1894). Although brick walls are transparent 
to these waves, they are reflected and refracted by certain 
other substances. It is with these rays that wireless teleg- 
raphy is carried on. By means of suitable receiving instru- 
ments, signals have thus been transmitted as far as fifty 
miles. 



CHAPTEE XXX 



POLARIZATION OF LIGHT 



327. Transverse Vibrations. — To understand polarization 
we must go back a moment to the nature of the light waves 
themselves. While we represent light rays as going out 
from a luminous body in all directions in perfectly straight 
lines, the real motion is in a plane at right angles to these 
rays, and in all possible directions. If we fasten a cord at 
one end, and, holding the other end in our hand, make the 
cord ripple in all possible planes, we shall have a rough rep- 
resentation of a real light ray. If the 

motion of the cord is projected upon the 
surface to which the end is fastened, we 
will have a series of radial lines, as 
shown in Fig. 239, which represents 
some of the planes in which the ether 
vibrates. To represent every possible 
plane of vibration, we should have to 
turn this circle of radiant lines into a 
solid black circle. In thinking, then, of a ray of light, we 
must think of it as vibrating in all possible directions, in 
a plane at right angles to its line of propagation. When 
such a ray passes through a homogeneous medium, like the 
ether, no particular result follows ; but when it passes 
through certain media to be described, we have the inter- 
esting phenomena of polarization. 

328. Polarization of Light. — A cord with one end fas- 
tened and the other end held in the hand may be rippled in 




Fig. 239. 



344 



PHYSIOS 



any and every plane so long as it passes freely through the 
air. If now it passes through a couple of vertical gratings, 
the ripples must all be in a vertical plane. Had the grat- 
ings been horizontal, only horizontal ripples would have 
been possible. If one grating be vertical and the other 
horizontal, no ripples can pass to the end of the cord, for 
only vertical ripples can pass the second grating ; conse- 
quently everything stops at the second grating, and beyond 
that there is no motion (Fig. 240). Something like this 
appears to happen in certain cases with light, and we call it 
polarization of light. 




Fig. 240. — Apparatus to illustrate polarization of light. 



To illustrate this we may cut two thin slices of tourma- 
line parallel to the axis of the crystal. These appear to act 
upon a ray of light as the gratings, represented in Fig. 240, 
act upon the vibrating cord. When these slices are arranged 
so that their axes are parallel, as in Fig. 241, a b, the ray of 
light passes through. If they are crossed obliquely, as in 
a' b\ we have partial extinction of the ray. If they are 
crossed at right angles, as in A B, we have complete extinc- 
tion of the light. We believe that when the ray of light 





POLARIZATION OF LIGHT 345 

passes through the first of these slices of tourmaline, all its 
transverse vibrations are cut off except those parallel to the 
axis of the crystal. A ray of light which has thus been 
robbed of all its vibra- a # 

tions except those in 0%. B A. 

one plane is said to be 
polarized, and the first 
crystal of tourmaline 

through which the ray Fig. 241.— Tourmaline polarizers and 
,, , , analyzers. 

passes is called a polar- 
izer. The second crystal of tourmaline is called an analy- 
zer, because it is by turning this at right angles to the 
other, and thus extinguishing the light, that we may deter- 
mine whether or not a ray has been polarized. 

Light may be polarized by reflection from a plane mir- 
ror. It is also polarized by refraction, and various sub- 
stances, such as Iceland spar or tourmaline, if cut in the 
proper manner, may serve as analyzers. If a ray of light 
make with the perpendicular to a mirror an incident angle 
of about fifty-seven degrees, the reflected ray will be 
polarized. 

329. Applications of Polarized Light. — If we arrange a 
projecting lantern so that we may introduce a polarizer and 
an analyzer (somewhat separated) between the condensing 
and converging lenses, we shall be able to exhibit the most 
interesting and beautiful phenomena of polarized light. 

By simply turning the analyzer, we may show the vary- 
ing degrees of light, from full illumination when polarizer 
and analyzer are parallel, to complete extinction when they 
are crossed. 

Geologists now study the rocks by making very thin 
sections, mounting them on glass, and then examining them 
by means of polarized light. By turning the analyzer we get 
a beautiful display of changing color. We may, by means 
of polarized light, test the genuineness of certain gems. 

Wonderfully beautiful experiments may be made by dis- 



346 PHYSICS 

solving any crystallizable compound, such as salicin or 
urea, in alcohol, spreading a film of the solution on glass, 
and introducing the glass, while still wet, between the 
polarizer and the analyzer. As the solution evaporates, 
tiny crystals appear on the plate, and with the turning of 
the analyzer we have the screen covered with a display of 
rare beauty and variety. 

330. Rotation of the Plane of Polarization— It is found 
that certain substances, such as quartz cut perpendicular 
to its axis, and certain solutions, such as sugar, when intro- 
duced between the polarizer and analyzer, rotate the plane 
of polarization. The amount the plane of polarization has 
been rotated is found by turning the analyzer. 

In the case of sugar, the angle depends upon the strength 
of the solution, and this gives us a convenient and accurate 
method of determining the strength of such solutions. 

It was Faraday's great discovery that a wave of polar- 
ized light may be rotated by means of a magnet. 

331. The Identity of the Various Forms of Radiation. — 
All forms of radiation may be polarized, may be refracted, 
may be reflected, and may be transformed, the one into the 
other. We believe that they differ from one another only 
in wave length, and consequently in the rapidity of vibra- 
tion. We believe that they are all rays of ether, having 
transverse vibrations. Those with longest wave lengths 
and slowest vibrations produce electrical phenomena, those 
with the next shortest wave length and next fastest vibra- 
tions produce heat phenomena, those with the next shortest 
wave length and next fastest vibrations affect the optic 
nerve with what we call light, and those with the shortest 
wave length and fastest vibrations are called chemical or 
actinic rays, "because of their power to effect chemical 
changes. As might be expected, all ether vibrations tend 
to effect chemical changes — that is, dissociate the atoms 
in the molecule ; and all ether vibrations tend to effect 
molecular motion, which is heat. 



SOUND 

CHAPTER XXXI.— General Principles 

332. Sources. 

333. Transmission. Figs. 242 and 243. 

334. Loudness — Re-enforcement. 

335. Pitch. Figs. 244, 245, 246, and 247. 
336 Quality. Fig. 248. 

337. Reflection— Echoes. Fig. 249. 

338. Velocity. 

339. Vibrations of Strings. Fig. 250. 

340. Sympathetic Vibrations. 

CHAPTER XXXII.— Music 

341. Music and Noise. 

342. The Scale. 

343. The Octave. Fig. 251. 

344. Vibration Ratio of the Musical Scale. Fig. 252. 

345. Musical Score Fig. 253. 

346. Melody. Fig. 254. 

347. Chords. Fig. 255. 

348. Harmony. Fig. 256. 

349. Counterpoint, Fig. 257. 

350. Reading Music. 

CHAPTER XXXIII.— Miscellaneous Application 

351. Speaking. Fig. 258. 

352. Hearing. 

353. Limits of Sound. 

354. The Phonograph. 

355. The Telephone. Fig. 259. 

347 



CHAPTER XXXI 

GENERAL PRINCIPLES 

332. Sources. — All sound-producing instruments must 
be in a state of rapid vibration. A tuning fork while pro- 
ducing a sound may be shown to be in vibration by touch- 
ing it to a pith ball suspended by a thread. The ball will 
bound away as if it had been struck ; and truly it has, but 
so quickly that our eyes can not see the blow. Or, if the 
prongs of a sounding fork be dipped into water it will 
throw a spray, and the fork will soon be brought to rest. 
A sounding bell, if touched with the finger, will instantly 
cease to produce sound. The long strings of the piano 
may be seen to vibrate while sounding. A pin or other 
light object will dance upon the sounding board while the 
piano is played, and a heavy organ pipe can be felt to be in 
vibration while producing a sound. 

333. Transmission. — In order that a sounding body may 
produce in our ears the sensation of sound, some medium — 
solid, liquid, or gas — must intervene. If we take the medium 
away, our sensation of sound ceases, no matter how vigor- 
ously the sounding body may keep up its vibrations. If, 
for example, we put a bell run by clockwork under the 
receiver of an air pump, and either suspend it by threads, 
or let it rest on thick wads of cotton or wool, the sound 
will grow fainter and fainter as the exhaustion proceeds, 
and will finally cease altogether when a vacuum has been 
attained. We are justified in believing that the medium is 
necessary for the transmission of sound, because when we 

349 



350 



PHYSICS 




6 o 



6 o 



Fig. 242. 



take the medium away the sound ceases to reach our ears. 
Experience teaches us that sounds are even more readily 
transmitted through solids than through gases. If one 

puts his ear against a 
long wire or a stick of 
timber, the scratching 
of a pin at the other end 
may be readily heard 
through the solid when 
it can not be heard at 
all through the air. So 
also liquids transmit 
sound more readily than 
gases. The denser the medium the more readily it trans- 
mits sound. Also the more elasticity a substance has the 
more readily does it transmit sound. Fig. 242, representing 
a number of billiard balls suspended in a row, each an inch 
or two from its neighbor, may serve to illustrate how sound 
is transmitted through the air or any other medium. Sup- 
pose the ball at one end of the line to be pulled one side 
and allowed to swing against its neighbor, the second ball 
will swing over and transmit the blow to the third ball, 
which will in turn pass on the blow to the next, and so on 
through the line. If these balls are of ivory or glass, or 
any elastic substance, the wave will quickly run through 
the line without much loss ; but if the balls are of some 
inelastic substance, as lead or putty, the impulse rapidly 
loses force. Thus it is that sound appears to be transmitted 
through any medium. The sound must be produced by a 
body in vibration — a column of air, as in the organ pipe 
and all wind instruments ; or a stretched string, as in the 
piano, violin, harp, and all stringed instruments ; or a 
membrane, as in the drum ; or a metallic plate, as in the 
cymbal, or in fact anything capable of vibration — and these 
vibrations are transmitted through the air to our ears, 
which are constructed so as to receive the impression and 



GENERAL PRINCIPLES 351 

translate it into our sensation sound, which is conveyed to 
the brain by the auditory nerve. 

Sounds differ so much that it is hard to realize that 
they all are the result of the vibration of the air. The air, 
being a perfectly elastic fluid, and transmitting pressure 
equally in all directions vibrates from a center outwardly 
in all directions. Suppose a disturbance to be set up at 
any one point, as, for instance, by the vibration of a bell 
(Fig. 213), the sides of the bell in vibration move first in 
one direction and then in the other, and the air receives 
the blows of the quivering metal in just the way that the 
pith ball did from the tuning fork (section 332) ; and not 
one blow, but many, up to two or three hundred in a second. 
Each time then the air receives a blow, it is compressed, 
and a spherical wave of compression is set up. But between 





Fig. 243.— Sound waves. 

each blow the metal draws back, and consequently sets up 
a similar spherical wave of rarefaction. A sound wave is 
spherical in shape, and consists of alternate spherical shells 
of compressed and rarefied air. There are three respects 
in which sounds differ : loudness, pitch, and quality. 

334. Loudness. — The harder we strike the tuning fork 
the louder its sound. If we examine its amplitude of vibra- 
tion, by dipping it into water, or touching it to a pith ball, 



352 PHYSICS 

we shall get a correspondingly vigorous fountain or lively 
blow. It must be that the vibrations of the loud-sounding 
body are more ample than those of the quieter body. If 
when the tuning fork is sounding very feebly it is dipped 
into water, the resulting splash will be found to be corre- 
spondingly feeble. Our entire experience leads us to believe 
that the loudness of a sound depends upon the amplitude 
of the wave that makes it — that is, upon the degree in 
which the air is compressed and rarefied. 

Re-enforcement. — The tuning fork set vibrating and 
simply held in the hand produces a very feeble note. To 
make it audible in a classroom or lecture hall, the fork 
must be held against some elastic body of larger surface, 
such as a wooden table top, a door, or an ordinary sound- 
ing-board. In this case the larger body is also set into 
vibration, and the surrounding air is more deeply affected. 
In most musical instruments we have such an arrangement 
for re-enforcing the sound, and to give it the volume needed. 

Loudness is seldom measured in any strict way. In 
music it is indicated by some word usually borrowed from 
the Italian, such as forte, loud ; fortissimo, very loud ; piano, 
soft ; pianissimo, very soft, etc. In physics it is represented, 
rather than measured, by the amplitude of the wave. The 
intensity of two sounds may be compared by observing the 
distance at which they may be heard. The sound wave, 
being spherical in form, is represented at any instant by 
the surface of a sphere whose radius is the distance from 
the sounding body. We know from geometry that the sur- 
face of a sphere is equal to 4 w r 2 . Hence the surface de- 
pends on r 2 , or the square of the distance. By the prin- 
ciple of virtual velocity, the original energy spread over this 
larger space must be less intense in exact proportion ; so 
we say that the intensity of any given sound varies inversely 
as the square of the distance. There is a slight variation 
from this, due to the fact that some of the energy of sound 
is changed to heat. 



GENERAL PRINCIPLES 



353 



OAA/VWVWWV 

Fig. 244. 



335. Pitch. — The term pitch is used in music and in 
ordinary speech to indicate the position of a sound in the 
musical scale. The pitch is high if the note is up toward 
the treble ; the pitch is low 

if the note is down toward Vl/l/WWW\AAAAA/\AAAAAAy 
the bass. And this is quite 
independent of loudness. We 
all know that women's voices 
have higher pitch than men's, 

and children's voices than older people's. However un- 
musical one may be, one is pretty sure to be aware of the 
fact that the notes on the right-hand side of the keyboard 
of a piano or organ are much higher in pitch than the 
notes on the left-hand side of the keyboard. The idea of 
pitch in sound is a perfectly definite one. Pitch trans- 
lated into vibration is equally definite. If two tuning forks 
of different pitch have a bristle attached to each, and if 
during vibration each bristle be allowed to trace a line by 
drawing the fork over smoked glass, it will be found that 
the tuning fork of higher pitch, the shorter fork, will trace 




Fig. 245.— Savart's wheel. 



a greater number of waves, giving evidence of being in 
more rapid vibration than the tuning fork of lower pitch, 
the longer fork (Fig. 244). We say then that pitch depends 
upon the number of vibrations per second. 

We may determine the number of vibrations which cor- 
24 




354 PHYSICS 

respond to any given pitch by various devices. One is 
Savart's wheel (Fig. 245), which consists of a large-toothed 
wheel capable of rotation, and provided with 
a flexible tongue against which the teeth 
may strike. The number of teeth, multi- 
plied by the number of turns per second, 
will give the number of blows the flexible 
tongue receives, and so the pitch of the 
Fig. 246. resultant note. The faster the wheel turns 

the higher the note. If, for example, we 
wish to measure the vibration frequency of a given tuning 
fork, we have only to set it into vibration, and then rotate 
the toothed wheel until it gives out the same note. An- 
other simple device is illustrated in Fig. 246. The disk is 
made to rotate in front of a tube through which a stream 
of air is passing. Each time a hole in the disk passes the 
end of the tube a puff of air passes through it. When the 
disk moves slowly we hear each separate puff; but when 
the disk moves so rapidly that we may not distinguish the 
separate puffs, we begin to recognize a tone which rises in 
pitch as the speed of the disk increases. By attaching to 
the disk a mechanism similar to that used in the cyclometer 
of a bicycle, we may, with watch in hand, count the num- 
ber of revolutions, and from that the number of puffs per 
second which correspond to a certain pitch of tone. When 
the tone compares in pitch to the middle C on the piano 
it is found to have two hundred and fifty-six vibrations per 
second. Fig. 247 represents an instrument for determin- 
ing pitch. It works upon the principle just stated, with 
some modifications in its mechanism. It is known as a 
siren. 

336. Quality or Timbre. — The Germans call this tone- 
color. If a note of given pitch be sung by two voices, or 
sounded by two instruments, say the piano and violin, it 
will be noticed that there is something distinctive about 
each note, and we can generally recognize the source of the 



GENERAL PRINCIPLES 



355 



note. It can not be a difference in the fundamental tone, 
as the pitch is the same in all four notes. Yet so real and 
subtle is it, that it makes one voice or instrument agreeable 
to our ear, and another voice or instrument disagreeable. 
Von Helmholtz, the great German physicist, investigated 
the matter very carefully, and found that this difference 




Fig. 247.— Siren. 



in the quality of sound is due to overtones or secondary 
sound waves that accompany the fundamental or major 
sound, and give it so characteristic a coloring that no two 
human voices, and no two instruments, even of the same 
class and make, ever sound precisely the same note. From 
a human and aesthetic point of view the quality of a sound 
is its most valuable character. The tuning fork gives an 



356 



PHYSICS 




Fig. 248— Helmholtz 
resonator. 



almost pure note, which, on account of its lack of shading, 
fails to be acceptable to the ear. Helmholtz was the first 
to measure the quality of a musical note by measuring the 
accompanying overtones. For this 
purpose he devised his resonators 
(Fig. 248), hollow globes of thin brass 
with openings on opposite sides, the 
smaller one for insertion in the ear, 
and the larger one for the reception 
of the sound impulse. The inclosed 
body of air will vibrate in sympathy 
with one special note only, and hence 
serves to detect that note in the midst 
of many others. By having a series 
of these resonators it is possible to 
detect the overtones accompanying any fundamental. This 
method gives, however, only a partial measure, since the 
total musical effect depends not alone upon the overtones 
themselves, but also upon their relative intensity. 

337. Reflection, Echoes. — If we place the chain of ivory 
balls represented in Fig. 249 so that the last one shall be 
near to a wall, and then send an impulse along the line by 
swinging the first ball against the second, this impulse 
will be reflected back 
by the last ball strik- 
ing against the wall and 
bounding back against 
its neighbor. In like 
manner sound waves in 
the air are reflected by 
walls of buildings, moun- 
tain peaks, etc. This is 
what we call the echo. 

338. Velocity.— The velocity of sound in air may be de- 
termined as follows : Two stations are selected at a known 
distance apart, and sharp noises, such as the report of a 




Fig. 249. 



GENERAL PRINCIPLES 357 

cannon or gun, are made at either or both stations, and the 
time that it takes for the sound to reach the other station 
is carefully noted. The time at which the discharge took 
place is known to the observer at the second station either 
by the flash or by an electric signal. Such experiments 
have been repeated very often and in different parts of the 
world, and while the results differ slightly, they all give 
nearly the same result, viz., about eleven hundred feet per 
second. We may count the seconds between the lightning 
flash and the sound of the thunder and calculate our dis- 
tance from the thunder cloud. We may see the steam 
pouring from the whistle of a distant steamship, and by 




Fig. 250.— Sonometer. 

counting the seconds before the sound is heard calculate 
its distance. 

It is evident that loudness, pitch, or quality have no 
effect upon velocity ; for when we hear a band of musicians 
playing at a distance the loud tones and the soft tones, the 
tones of high pitch and low pitch, and the tones of vari- 
ous quality, if played simultaneously, all reach the ear 
together. 

339. Vibration of Strings. — A useful and standard in- 
strument for examining the vibrations of strings is the 
sonometer, or monocliord (Fig. 250). A stretched string, 
capable of vibrating under varying tensions and lengths, 



358 PHYSICS 

and capable of being replaced by other strings, is re-en- 
forced by a sounding box made of dry, elastic wood. By 
means of this instrument the following laws may be illus- 
trated and verified : 

1. Pitch varies with the material of the string. 

2. Pitch varies inversely with the length. 

3. Pitch varies inversely with the diameter. 

4. Pitch varies with the square root of the tension. 
We may sum this up by saying that strings which are 

heavy, long, thick, and slack, give a low note, while strings 
which are light, short, thin, and tense, give a high note. 

In the piano the strings are tightly stretched — steel wire 
for the treble, and steel wire wrapped around with copper for 
the bass. The keyboard is fixed, and when a key is struck 
the blow is transmitted by means of levers and hammers to 
the corresponding string. The wires are stretched between 
iron pins fastened to the frame of the instrument. The 
length of the wire is determined by the position of the 
agraffe, or bridge, which rests directly upon the large spruce 
sounding-board that forms the bottom of the piano box. 
The instrument is tuned by turning the pins and so chang- 
ing the tension of the strings. The position of the ham- 
mers is a matter of great importance, since the blow on 
the strings determines the overtones. In most pianos the 
strings are struck at a distance of one seventh, one eighth, 
or one ninth from the end, so as to bring out the desirable 
overtones. Different pianos differ in sweetness and tone 
largely because of their overtones and the greater or less 
efficiency of their sounding-boards. 

A modern grand piano, such as the Steinway, contains 
forty thousand separate pieces of material. The piano, in 
spite of many musical defects, is a singularly rich- instru- 
ment, since it offers such large opportunities for the play 
of harmony. Not only may several notes be struck at once 
in a given chord, but the combination of two parts — the 
bass and treble — allows added richness and variety. 



GENERAL PRINCIPLES 359 

In other stringed instruments, such as the violin and vio- 
loncello, the vibrations are induced by means of a rosined 
bow, and the sound is re-enforced by a box beneath the 
strings, a box which is of all forms for acoustical re-en- 
forcement the most perfect in design. The much-prized 
instruments of Stradivarius, Amati, and Guarnerius, owe 
their value to their perfect form, to the elasticity of their 
well-seasoned wood and marvelous varnish, and, some per- 
sons think, to the fact that several subsequent generations 
of master violinists have induced in them the " habit " of 
harmonic vibration. Musically, the violin is much superior 
to the piano ; the single notes are far richer by reason of 
the full set of harmonics present, and particularly of the 
higher harmonics. 

340. Sympathetic Vibrations. — The richness of the organ, 
piano, and other musical instruments is due not only to 
the overtones accompanying the fundamental note, but also 
to a second group of accompanying notes due to what is 
called sympathetic vibration. If two tuning forks of the 
same pitch, and mounted on suitable resonator boxes be 
placed near each other and one of them set in vibration, 
it can readily be shown that the second untouched fork is 
also vibrating. A pith ball brought in contact with the 
fork will be thrown aside ; or, if the original fork be 
silenced, the second fork will be found emitting an unmis- 
takable note. Had the forks been of different pitch, no 
such sympathetic reaction would have taken place. Simi- 
larly, if the loud pedal be pressed down, and a strong, pure 
note be sung into a piano, the string corresponding to that 
note will be set into vibration. 



CHAPTEE XXXII 

MUSIC 

341. Music and Noise. — We know the sensation differ- 
ences between music and noise. The one pleases by its 
regularity and rhythm and by a certain anticipatory quality 
which leads us to expect a given effect, and then gratifies 
our sense of anticipation by giving us the effect. The other 
displeases us, and the more so the more sensitive our organi- 
zation. It displeases by its irregularity. It must be said, 
however, that the line between music and noise is not a 
hard-and-fast one, even to musicians. There are certain 
passages in the compositions of Wagner and of the more 
stormy Eussian artists which are music to one school of 
musicians and noise to another school. However, we all of 
us know in general the sensation differences between music 
and noise. A vibrating tuning fork gives an undoubted 
musical note of very pure quality, while a door slammed 
gives a decided noise. The tuning fork vibrates regularly, 
giving so many perfect waves per second, and, as we have 
seen, traces an even, symmetrical line on smoked glass. If 
a visiting card is drawn slowly over the teeth of a saw we 
hear the successive taps or noises of the card striking 
against the teeth of the saw ; but if the card is moved very 
rapidly, so that we may no longer recognize the distinct 
taps, the noise begins to assume the character of a tone. 
So it is with the puffs of the siren (335) ; so it is also with 
the sound of a buzz saw. 

342. The Musical Scale. — All nations have made such a 
selection of musical notes, and have framed them into a 

360 



MUSIC 



361 



series known as the musical scale. This has varied greatly 
in historic times, and even now we may not regard it as 
quite fixed. The Greeks had what seems to us now a very 
meager and almost unmusical scale. It was, however, care- 
fully thought out, and has practically formed the basis of 
all modern music. The scale was greatly enriched during 
the middle ages, and particularly when music came into 
such large service in the Church. The sacred music of 
mediaeval times, especially in Italy and Germany, made great 
and rapid advance toward modern perfection. All this 
work, however, was purely art work, and not as yet science. 
The musical scale that has thus come down to us is a 
product of the rich, emotional, and aesthetic life of the 
world, and not of its thought. The older musicians knew 
nothing of acoustics, knew nothing of vibration numbers, 
and sound waves. They knew only what pleased the heart 
and expressed its reverence and delight. 

343. The Octave. — Pitch depends solely upon the num- 
ber of vibrations per second ; but as soon as we begin to 
compare notes of definite pitch with one another we are 



HIWIWWIWWillWWIW MlWIiff 



A 4 B 4 C 3 


C 2 


c x 


c 


c 


C" 


c 1 " 


C ,V 


.6 §30 32 


64 


128 


256 


512 


1024 


2048 


4096 



Fig. 251.— The piano keyboard. 



struck with the fact that when we have gone a certain dis- 
tance in either direction the notes appear to be repeating 
themselves. They are higher or lower, it is true, but they 
have the same musical character. A corresponding rela- 
tion is found to exist between their vibration frequencies. 
Taking the note C, making 256 vibrations per second, it is 
found that the next note above it, C 1 , that has the same 
musical character, makes 512 vibrations, or just twice as 
many as C. Above that the next similar note is C n , with 
1,024 vibrations. Then comes G m with 2,048 and C IV with 



362 PHYSICS 

4,096 vibrations, and we reach the upper limit of the piano. 
Had we gone down instead of up, we should have found the 
first lower note similar to to be C l5 making just half the 
number of vibrations, or 128. Below that comes C 2 , with 
64 vibrations, and still below that C 3 , very far down among 
the thunderous notes of the bass, and making only 32 vibra- 
tions per second. This is very near the lower limit of 
musical sound. C 3 to C IV covers about the range of an 
ordinary piano keyboard (Fig. 251). Between C and C 1 
custom has introduced six notes, and we designate them by 
the letters of the alphabet— D, E, F, G, A, B. The scale 
thus repeats itself every seven notes. This group of eight 
notes is called the octave. C n is two octaves above C ; C IV 
is four octaves. Similarly, C 3 is three octaves below C. 
The scale may begin on any note of the octave, but it will 
be best to regard the scale beginning with C as a type. 

344. Vibration Ratios of the Musical Scale. — If we take 
the number of vibrations of the fundamental note of the 
scale as unity, then its octave will be 2, and the interven- 
ing notes as follows : 

C D E F G A B C (1) 
do re mi fa sol la si do (2) 

1 I I I I I V- 2 (3) 
256 288 320 341 £ 384 426| 480 512 (4) 

(1) is the usual musical notation ; (2) is the notation com- 
monly used in singing ; (3) is the vibration ratios which hold 
for the scale whatever its position on the keyboard ; and 
(4) is the working out of these ratios for the octave, begin- 
ning with the middle C. 

Intervals. — When we look closely at such a scale we see 
that the intervals are not all equal. The intervals between 
mi and fa and between si and do are called half tones, and 
the other intervals are called whole tones, although the 
" whole tones " are not equal to each other, nor are the so- 
called half tones half of any one of them. On the piano 



MUSIC 



363 



keyboard each of the so-called whole tones are divided into 
halves by the black keys (see Fig. 252). This enables one to 



I II III II III Hill II III il III II III II III 

I I ii ITi i ii Mini ill in 1 mill 1 ! imili i iTTh 1 1 111 

.B.C. c c, c c 1 c" c m 



A 4 B,C 3 


C 3 


C! C C 


C" 


26 f30 32 


64 


128 256 512 

Fig. 252. — Piano keyboard. 


1024 



begin with do on any letter and bring in the half step 
between m i and fa. 

345. Musical Score. — It is the custom to represent mu- 



sical notes by conventional signs — 



& & 



I I s fc fc * 

s S * 



which are read whole note, half note, quarter note, eighth, 
sixteenth, thirty-second, and sixty-fourth. These terms 
apply, not to the tone intervals, but solely to the time to 
be given to each tone. Five parallel lines constitute the 
staff on which the 

notes are to be /"• --^-f- 

placed, and the po- 
sition of the notes 
on the staff indi- 
cates their pitch. 
When the staff will 
not accommodate 
all the score, addi- 
tional lines, called 
ledger lines, are em- 
ployed. In music written for two hands, as the score for 
piano and organ, separate conventions are used ; for the 

right hand the treble clef, 3£ and for the left hand the 
base clef, 2z Fig. 253 represents the position of the 

letters upon the score. 

346. Melody. — The art of musical composition is per- 
haps the supreme act of which the human mind is capable. 




Fig. 253. 



364 



PHYSICS 



The earliest composition was naturally the simple arrange- 
ment of sounds in pleasing succession, and for this sequence 
of sound the term melody has long been used. The arrange- 
ment and the effect are both simple ; one sound is followed 
by another according to no perceived physical law, but 
solely, perhaps, in accordance with some aesthetic law by 
which the succession gives us pleasure. Some of our most 



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Fig. 254.— Theme from Beethoven's Fifth Symphony. 

touching music, our folk songs, ballads, and the like, are 
pure melody. So, in more complicated music, melody is 
sometimes introduced by way of contrast or relief, or to 
emphasize, by its very simplicity, a leading thought in 
the composition. Wagner nearly always introduces the 
characters in his operas by such a melody, or " Leit-motif." 
A simple melody is often used as the theme or text out of 
which more elaborate music is to be developed. The above 
example of very beautiful melody is the theme of the slow 
movement of Beethoven's Fifth Symphony (Fig 254). 

347. Chords. — Melody is simplicity itself, for, while it 
may please in greater or less degree, it can never absolutely 
displease, because it can never be other than musical. But 
the possibilities of music would be ill explored if we con- 
fined ourselves to a mere succession of musical sounds, 
however agreeable they might be. There are tremendously 
greater possibilities when we come to sound several notes 
at the same time. Two or more notes sounded simultane- 



MUSIC 365 

ously constitute a chord. If the effect is agreeable, we call 
it concord ; if disagreeable, discord. 

The simplest chords contain but two notes, as the 
octave, C C ; the perfect fifth, G ; the fourth, C F ; the 
major third, C E ; the major sixth, C A, and the less agree- 
able minor third, minor sixth, etc. These binary combina- 
tions form the basis of our musical analysis, since chords of 
three or more notes may be resolved into their binary chords. 

The most important chord in music is the major triad, 
C E G, or common cliord, which may be considered as made 
up of a major third, C E ; a minor third, E G ; and a per- 
fect fifth, C G. By substituting C for C, we get the cliord 
of the sixth, EGC; and by the further substitution of E' 
for E, we get the chord of the sixth and fourth, G 0' E\ 
These three chords are all agreeable, but produce somewhat 
different musical sensations. 

Harmonics. — The quality of a musical note depends, as 
we have seen, upon the overtones. The upper harmonics 
are too faint to be appreciable, but the lower ones are very 
important. When we strike C, we have the following suc- 
cession of notes : 

C C G' C" E" Gt", etc. 
12 3 4 5 6, etc. (vibration ratios). 

We may discard all above G", and represent it thus 
(Eig. 255) : In the harmonics of this one note we have 
already present the principal chord of _ i9m 

music, the octave, C C ; the perfect fifth, ^ 

C G' ; the fourth, G' C" ; the major third, ih Z 

C" E" ; the minor third, E" G". This may Sp===z 
account for the fact that these chords are FlG 255 

agreeable, since they merely emphasize 
notes already present in the fundamental. In general, notes 
to be harmonious must have vibration frequencies that 
stand to each other in a simple ratio. There is, however, 
conflict between the two series of harmonics. 



366 



PHYSICS 



348. Harmony. — The highest expression of musical art 
is in harmony, which is the combining of many sounds into 
one agreeable composition. It is practically a progression 
of chords, groups of notes sounded in such orderly succes- 



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Fig. 256. — Illustration of harmony from Schumann's Nachtstuck, No. 4. 



sion as to produce the impression of unity and purpose. 
The laws of harmony are very intricate, and presuppose an 
acquaintance with elementary music. The above bars from 
Schumann's Nachtstiick is a beautiful illustration of har- 
mony (Fig. 256). 

349. Counterpoint. — As harmony is the highest expres- 
sion of music, so counterpoint is the highest expression of 
harmony. In counterpoint we have harmony brought about 
by the combination of two or more me]odies, a combination 
which yields the fullness and satisfaction of harmony with 
the movement and life of melody. The great master of 
counterpoint was Sebastian Bach (1685-1750). The accom- 
panying excerpt from Palestrina illustrates counterpoint 




WOLFGANG AMADEUS MOZART (1756-1791). 

One of the greatest musicians the world has produced. While a 
mere lad he played before nearly all the sovereigns of Europe. 
"His music from the first to the last has been most highly appre- 
ciated." 



MUSIC 



367 



(Fig. 257). Handel, in England, and other masters of the 
seventeenth and eighteenth centuries brought counterpoint 
to a perfection that it has never since reattained. It occu- 
pies, indeed, a very subordinate part in the compositions of 
the nineteenth century, which are mainly engaged in ex- 
ploiting the possibilities of harmony. But as harmony 



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— 



J i I ,i J: m i 






etc. 

! 



-3-« 



w {g 



v-i — 



Fig. 257. — Illustration of counterpoint. 



grew out of counterpoint, so it now seems probable that a 
more magnificent counterpoint will grow out of our enlarged 
knowledge of harmony. The tendency to return to coun- 



368 PHYSICS 

terpoint is shown in the work of such modern composers as 
Mozart and Mendelssohn. 

It has been well said that melody gives one the idea of 
motion, and harmony the feeling of rest. Melody must 
progress, or it ceases to be melody, but a simple harmonious 
chord is complete and perfect in itself. In modern counter- 
point we have the strength of both, the movement of the 
contrasted melodies and the restful background of their 
underlying harmony. 

Our ideas of musical beauty are so variable that it seems 
impossible to reduce them to strict physical statement. 
Taste changes, and each new master gives greater flexibility 
to the material of music. To the complaint that one of 
his works contained a certain passage that was not allowed, 
Beethoven replied : " Then I allow it j let that be its justi- 
fication." 

350. Reading Music. — It might well be a part of every 
liberal education to learn to read music intelligently. There 
are people who read music so easily, and construct it in 
their minds so vividly, that they get as great pleasure in 
simply turning over the leaves of a musical composition as 
we do in glancing over a favorite poet. 



CHAPTEE XXXIII 



MISCELLANEOUS APPLICATIONS 




351. Speaking. — The opening between the vocal cords is 
called the glottis, and is practically a slit, somewhat like 
the lip of an organ pipe. When no sound is produced, the 
vocal cords are far apart, and 
the glottis takes the shape of 
a V, with the wide part behind. 
When voice is produced, the 
vocal cords are drawn together 
under some tension, their edges 
are parallel, and the glottis be- 
comes a mere narrow slit (Fig. 
258). The pitch of the emitted 
sound depends on the tension 
of the vocal cords. As this is 
controlled by the muscles of the larynx, we can alter the 
pitch of our voice at will, but only, of course, within some- 
what narrow range. 

The character of the voice depends on small structural 
differences in the larynx. In women and in boys the voice 
is higher, simply because the vocal cords are shorter, and 
hence vibrate a greater number of times per second. In 
the same way, soprano and alto voices in women, and tenor 
and bass voices in men, result from the size and tension of 
the vocal cords. A trained singer, by altering the tension 
of the cords, can cultivate great flexibility. This control, 
like the control of nearly all our faculties, is best acquired 
when we are young. 

25 369 



370 PHYSICS 

This accounts, however, only for the voice itself, and 
not at all for speech. The animals have a very similar 
apparatus for producing sound, and, in the case of the birds, 
they use it very skillfully. 

In speech the voice has to have a very definite charac- 
ter, and many modifications, in order to express all our 
varying shades of meaning. The primary speech sounds, 
vowels and consonants, are brought about by changing the 
shape of the cavity of the mouth, an operation depending 
mainly on the tongue and lips. This change in the quality 
of the tone is due, physically speaking, to the overtones 
which are produced by the varying form of the mouth. 
The character of the sounds, as elements of speech, is quite 
independent of the tension of the vocal cords. 

The human voice only covers a range of about two oc- 
taves. Few people in ordinary speech cover one octave. 
The rising inflection at the end of a question sometimes 
amounts to a fourth ; the falling inflection at the end of a 
simple sentence to a fifth, and even emphasis, where pro- 
duced by a change of pitch, seldom exceeds a fifth. The 
cultivation of a greater range would add much to our power 
of expression. 

In singing, the sound itself is the great thing, and the 
words quite secondary. The great operas are sung in 
Italian, because of the greater wealth of vowel sounds in 
that language. In some modern music no words are used 
at all. A simple vowel sound is selected, and the musical 
effect gained by variations of pitch and time. In this case, 
the voice is treated as a simple musical instrument, and 
not at all as an organ of speech. The physical process of 
singing depends for its success mainly on the flexibility 
and control of the vocal cords, and upon the ability to pro- 
duce a sustained and uniform blast of air through the glottis. 
In the best systems of modern voice culture, this flexibility 
is the main thing sought for, and the " singing voice," as 
it is well called, is cultivated both for speech and song. 



MISCELLANEOUS APPLICATIONS 371 

In compass, the human voice ranges from about F 2 in 
the base (86 vibrations) to about F 1 in the treble (768 vibra- 
tions). Exceptional soprano voices have gone as high as 
E 11 (1,280 vibrations). One voice is seldom able to cover 
more than two octaves. 

352. Hearing is physiologically the reverse process of 
speaking. Speech begins in the brain as a thought, passes 
to the muscles of the larynx, tongue, and lips as a nerve 
impulse, and emerges into space as an air vibration. Hear- 
ing, on the contrary, depends for its stimulus upon an air 
vibration, which is transmitted by the ear as a sensory im- 
pulse, and ends in the brain with thought. Hearing, there- 
fore, consists of three distinct processes — excitation, trans- 
mission, and interpretation. The excitation consists in a 
sound wave impinging on the drum of the ear. The sound 
wave is usually of the air, but it may also be of the water, 
if we put our ear beneath the surface. The excitation may 
also be produced by direct contact with a vibrating solid 
body, as when a sounding fork is held against the bridge of 
the nose, or against the teeth. But in general the excita- 
tion is aerial, and strikes the ear drum. Here a whole series 
of wonderful things happen. The ear drum is a stretched 
membrane, very thin and very strong. It will bear the 
pressure of a column of mercury fifteen inches high — that 
is, an extra pressure of half an atmosphere. This ear drum 
or membrane separates the outer ear from the drum cavity. 
In this there are three small and delicately poised bones 
which receive the vibrations of the ear drum, and pass them 
on to the inner ear, and so, by means of the auditory nerve, 
to the brain itself. 

The act of transmission is a very complicated one, in- 
volving as it does so many distinct physiological parts — the 
external ear, the external auditory canal, the drum mem- 
brane, the middle ear with its three tiny bones, and the 
ventilating canal that leads to the back of the mouth ; the 
Eustachian tube ; the internal ear with its wonderful canals 



372 PHYSICS 

and processes ; and finally the auditory nerve going directly 
to the temporal lobes of the brain. 

But even more wonderful than this process of transmis- 
sion is the interpretation of the nerve impulse into signifi- 
cant sound, when it reaches the brain, and about this we 
know absolutely nothing at all. 

353. Limits of Sound. — As a sensation, sound is limited. 
The human ear will not respond to those which have more 
than 40,000 vibrations per second. Many persons can hear 
nothing above about 12,000 vibrations, and consequently 
do not detect the squeal of a mouse or the cry of a bat. 
We are all deaf to many of the shrill sounds of the insect 
world. Some animals are believed to be able to hear sounds 
that quite escape our own ears. 

Music employs only the lower notes, from about A 4 (27-J 
vibrations) to C IV (4,224 vibrations) on the piano, and up 
to D IV (4,752 vibrations) on the piccolo. The middle is 
counted at 256. 

354. The Phonograph. — No scientific instrument in its 
day has excited greater interest than Mr. Thomas A. Edi- 
son's phonograph, or sound-recording apparatus, invented in 
1878, and first apprehended as a scientific toy, but since 
brought forward as a serious servant in the affairs of every- 
day life. The phonograph consists in a horizontal axle 
capable both of rotation and of longitudinal advance. On 
this is mounted a cylinder, covered in the early days with 
tin foil, but now made with some plastic composition for 
its surface. A fixed mouthpiece is mounted over one end 
of the cylinder, when the axle is at its extreme position. 
The mouthpiece has a flexible diaphragm, provided at the 
center of its rear face with a small, sharp stylus, which 
presses against the plastic surface of the cylinder. 

When talking into the machine the cylinder rotates, 
and also slowly advances, so that a fresh portion of its sur- 
face is constantly passing under the stylus. Imagine the 
mouthpiece in position, and the cylinder slowly rotating. 




SIR WILLIAM THOMSON (1824- 
(Lord Kelvin.) 



MISCELLANEOUS APPLICATIONS 373 

Any sound waves striking against the diaphragm set it into 
vibration, and the little stylus no longer traces an even 
groove on the surface of the cylinder, but a groove which 
is now of varying and constantly changing depth. Every 
sound is thus recorded in these minute characters on the 
surface of the cylinder, and may be reproduced by throwing 
back the mouthpiece, bringing the cylinder back to its 
original position, adding a suitable speaking trumpet to the 
mouthpiece, and then repeating the motion of the cylinder. 
The little stylus, passing over its own tracing, moves in and 
out with the varying depth of the groove, and so produces 
in the diaphragm vibrations similar to those originally in- 
duced in it. The trumpet strengthens these sound waves, 
and we have a reproduction of the speech or music curiously 
like and curiously unlike the original. 

Uses of the Phonograph. — It was hoped that the phono- 
graph might be used in place of dictation, both by editors 
and busy letter writers, the cylinder being sent at once to 
the printing office, or mailed to the correspondent at the 
other end, but this practical use of the phonograph has not 
yet been realized. It remains chiefly as an amusement for 
the curious in our big cities and popular resorts. 

A much more important use than this would be the 
application of the phonograph to the reproduction of books, 
so that the blind could be read to, and all of us, tired per- 
haps with the day's work, and willing to save our eyes of 
an evening, could hear our favorite author read. When 
we went to buy such books, the shopkeepers would ask us, 
not whether we preferred the Avon edition, or the Eiver- 
side, or the half calf or morocco, but simply whether we 
preferred Mrs. Scott Siddons's rendition, or Mr. Horace 
Howard Furness's, or Mr. Eobertson's, or some other good 
reader's. 

355. The Telephone means sound at a distance, and is 
one of the most important of modern sound instruments. 
The acoustic telephone is only a box, but its principle is 



374 



PHYSICS 



worth considering. The transmitter and receiver are alike 
simply a little cylinder of wood or metal having one end 
open and the other end closed by parchment or other flex- 
ible diaphragm. A fine wire or string leads from the center 
of the diaphragm of one instrument to the center of the 
diaphragm of the other. The wire or string must pass 
freely from one instrument to the other, and must be mod- 
erately taut. When you speak into one cylinder, the trans- 
mitter, the diaphragm is set into vibration, and these vibra- 
tions produce corresponding longitudinal vibrations in the 
wire or string, and so in turn are transmitted to the dia- 
phragm of the receiver. Here they produce vibrations of 




Fig. 259. — Telephone receiver. 



the air similar to the original sound waves. If the receiver 
be held to the ear, the message is distinctly heard over a 
distance of several hundred feet. 

The magneto-telephone depends upon both acoustical 
and electrical principles, but with a little care may be read- 
ily understood. Kemove the top of a regular telephone 
receiver and examine its construction, or else consult the 
accompanying figure (259). There is a flexible diaphragm 
or disk, D, made of thin iron, and directly back of this disk 
a steel bar magnet, running the length of the instrument. 
The end of the magnet nearest to the disk is surrounded 
by a coil of fine insulated copper wire, i?, whose ends are con- 



MISCELLANEOUS APPLICATIONS 375 

nected with the binding posts, C, on the far end of the tele- 
phone receiver, and through those with the line wire. This 
instrument may serve either as transmitter or receiver, 
though it is now only used in practice as a receiver. When 
you speak into the telephone, the iron diaphragm is set into 
vibration, and currents of electricity are induced in the coil 
of copper wire (Fig. 259). The direction of these currents 
varies with the approach and recession of the diaphragm, 
and produces variations in the strength of the magnets at 
each end of the lines. These variations set up correspond- 
ing vibrations in the diaphragm of the receiver at the farther 
end of the line ; the air is thrown into corresponding vibra- 
tions, and so brings the sound to the ear. The acoustic 
principle of the Bell telephone is very similar to that of 
the acoustic telephone, except that the vibrations are trans- 
mitted not directly as a pulsation of the string, but indi- 
rectly as a varying current in the wire. The electricity 
simply acts as the carrier of the energy. In the transmitter 
the sound energy is transformed into electric energy, and 
this, in the receiver, is retransformed into sound energy. 
Such a telephone is in reality a magneto-electric machine. 
For this and the modern form of the telephone see sec- 
tions 266 and 268. 



INDEX 



Absolute cold, 199. 
Absolute temperature, 199. 
Absolute zero, 199. 
Absorption, 186. 
Acceleration, 49. 
Accumulation of electricity, 248. 
Adhesion. 18. 
Air, buoyancy of, 114. 

compressor, 132. 

gun, 124. 

pump, 130. 

thermometer, 162. 

weight of, 106. 
Alcoholometer, 102. 
Alloys affecting fusing point, 166. 
Alternators, 282. 

Altitude determined by ther- 
mometer, 172. 
Amati. 359. 
Ammeter. 264. 
Ammonia, 201, 203. 
Amorphous, 17. 
Ampere, 261. 

Ampere, Andre Marie, 261. 
Analyzers, 345. 
Angles of incidence and reflection, 

304. 
Animal heat, 151, 204. 
Animals, cold-blooded, 163. 

warm-blooded, 163. 
Anode, 239. 



Antimony, 284. 
Archimedes, 103. 

principle of, 98. 
Arc lamp, temperature of, 295. 
Aristotle, 106. 
Armature. 280. 

Arrangement of battery cells, 268. 
Aspirating siphon. 134. 
Astigmatism, 332. 
Atmosphere, 9, 105. 

density at different heights, 112. 

pressure of, 108. 

pressure on human body. 126. 

variations in pressure, 109. 
Atoms, 8. 
Axioms, 75. 

Bacchus illustration, 123. 

Bach, Sebastian, 366. 

Balance, 40. 

Balloons, 115. 

Barium, platino-cyanide of, 339, 

340. 
Barium sulphide, 339. 
Barometer, aneroid, 109. 

Fortin's, 109. 

mercury. 107. 

tension inside, 137. 
Battery cells. 245. 

in parallel, 269. 

in series, 268. 

377 



378 



PHYSICS 



Beethoven, 364, 308. 

Bichromate cell, 242. 

Bismuth, 284. 

Black keys of piano, 3(53. 

Blowing engines, 132. 

Blushing, 204. 

Bodies, simple and compound, 7. 

Boiler rivets, 154. 

Boiling, 169. 

laws of, 170. 

on mountain top, 204. 
Boiling point affected by altitude, 
172. 

affected by nature of containing 
vessel, 171. 

affected by pressure, 171. 

changes of, 170. 

of water, 149. 

table of, 170. 
Bottle imp, 121. 
Boyle's law, 112. 
Brittleness, 19. 
Brooklyn Bridge, 155. 
" Brush," 281. 
Bulging walls, 154. 
Bunsen cell, 242. 
Buoyancy, 96. 

Caissons, 124. 

Calcium tungstate, 340. 

Calipers, 31. 

Caloric, 192. 

Candle power of various lights, 

294. 
Candle, standard, 293. 
Capillarity, 22. 
Carbon dioxide, 135, 202. 

liquefying, 169. 
Carre ice machine, 201. 
Cartesian diver, 121. 
Casting metals, 165. 
Cataract, 332. 



Cathetometer, 32. 
Cells in parallel, 246. 

in series, 245. 
Celsius, 158. 

Center of oscillation, 63. 
Centigrade scale, 158. 
Centimeter, 25. 
C.-G.-S. system, 26, 52. 
Change of state by heat, 152, 153, 

164. 
Change of volume by fusion, 165. 
Change of volume by heat, 153. 
Changes, physical and chemical, 

10. 
Charles, law of, 161. 
Chemical effects of electricity, 248. 
Chemical rays, 339, 346. 
Chemistry, 4. 
Chords, musical, 364. 
Clark Brothers, 331. 
" Clatter " bell, 257. 
Clausius, 147. 
Clef, 363. 
Clothing, 180. 
Cloud banners, 176. 
Clouds, 172. 
Clouds at sunset, 312. 
Coefficient of expansion, 153. 

of gases, 161. 

irregularities, 156. 

table of, 154. 
Cohesion, 17. 
Coil, telephone, 276. 
Cold by evaporation, 200. 
Cold by expansion of gases, 200. 
Collecting apparatus, 281. 
Color, 335. 

Color and temperature, 339. 
Colors, complementary, 336. 

in sunlight, 338. 
Color wheel, 337. 
Combustion, 150. 



INDEX 



379 



Commutator, 259. 281. 

Compass, spring, 31. 

Complementary colors, 336. 

Compost heaps, 151. 

Compound microscope, 330. 

Compounds. 8. 

Compressed-air motors. 123. 

Concave mirrors, 306. 

Condensation, 177. 

Condensers of electricity, 230. 

Conduction of heat, applications 
of, 180. 

Conductivity of heat, table. 179. 

Conductors of electricity, 223, 260. 

Conjugate foci. 306. 

Convection, 182. 

Convex mirrors, 309. 

Cooking by electricity, 151. 

Counterpoint, 366. 

Couple, 68. 

Critical angle, 320. 

Critical temperature, 168. 

Crystals. 155. 

Crystalline form. 16. 

Crystallization. 177. 

Curved image from straight ob- 
ject, 310. 

Curvilinear motion, 50. 

Dalton, 15. 

Daniell cell, 243. 

Davy. Sir Humphry, 147. 

Daylight, how diffused, 311. 

Decimeter. 25. 

Declination of magnetic needle. 

215. 
Deliquescence, 197. 
Densities, table of, 42. 
Density. 42. 
Dew on grass, 175. 

on ice pitcher, 175. 
Dew Point. 172. 



Dial thermometers, 154. 
Dialysis, 21. 
Dialyzer, 21. 
Diffusibility, 20. 
Diffusion, 20. 

Diminished images in convex mir- 
ror, 309. 
Dipping needle, 214. 
Distances, how estimated from 

visual angle, 296. 
Distribution of plants and animals, 

163. 
Divided circuits, 269. 
Diving bell, 124. 
Double boiler, 204. 

pump, 129. 

windows, 180. 
Draper, 295. 
Drawings upon highly polished 

surfaces, 315. 
Ductility, 19. 
Dynamo. 278, 284. 
Dyne, 52, 70. 

Ear, 371. 
Eardrum, 124. 
Earth a magnet. 214. 
Earth as seen from the moon, 313. 
Earth's shadow, 299. 
Echoes, 356. 
Eclipses, 298, 301. 
Edison, Thomas A., 372. 
Effect of an electric current upon 
a magnetic needle, 254. 

of heat and cold on rocks, 155. 
Effects of electric currents, 246. 
Elasticity, 18. 
Electrical distribution, 232. 

effects of points, 232. 

machines. 230. 
Electric and cable cars, 282. 
Electric bell. 256. 



380 



PHYSICS 



Electric conductors, 260. 

currents by mechanical means, 
278. 

by heat, 284. 

sources of, 235. 

furnaces, 247. 

gas lighting, 275. 

light, 247. 

measurements, 259. 

motor, 257, 259, 284. 

potential, 237, 260. 

stove, 247. 

waves, 290, 346. 

welding, 248. 

whirl, 234. 
Electricity and steam, 282. 
Electricity for transmitting power, 

283. 
Electrification, two states of, 222. 
Electro-chemical series, 239. 
Electrolysis of salts, 250. 

of water, 249. 
Electrolytic assay, 251. 
Electro-magnet, 253. 
Electro-motive force, 237. 
Electrophorus, 228. 
Electroplating, 251. 
Elements, 7. 

table of, 12. 
Ellipse, 51. 
Energy, 32, 71. 

kinetic and potential, 72. 

transformation of, 72. 
Enlarged images by refraction, 324. 

in concave mirrors, 307. 
Erg, 70. 

Ether, 3, 54, 184, 185, 211, 220, 226, 
280, 295, 339, 340, 342, 346. 

flow, 253. 

stress, 253. 

vibrations, 290, 292. 

vortex, 251, 253. 



Eudiometer, 10. 
Eustachian tube, 125. 
Evaporation, five factors of, 166. 

of snow and ice, 167. 

of solids, 167. 

produces cold, 200. 
Expansion by heat, applications of, 
154. 

of crystals, 155. 

of gases, correction of volume 
for temperature, 161. 

of glass, 158. 

of ice, 155. 

of liquids, 156. 

of rocks, 155. 

of solids, 153. 

table of, 154. 
Explosion by superheated steam, 

171. 
Explosives, 123. 
Extension in one direction, 30. 

in two directions, 33. 

in three directions, 34. 
Extra currents, 275. 
Eye, 331. 

Fahrenheit scale, 159. 

Falling bodies, 56. 

Faraday, 278, 346. 

Faraday, Michael, portrait of, 207. 

Far-sightedness, 333. 

Filtering colors, 340. 

Fire extinguishers, 123. 

Fireplace, i85. 

Floating bodies, 'stability of, 104. 

Fluids, 89. 

in motion, 139. 
Fluorescence, 338. 
Focal distance of a lens, 326. 
Fog, 172, 176. 
Foot pound, 71. 
Force, 32. 



INDEX 



381 



Force of crystallization, 165. 

pump, 128. 
Fountain ink wells, 138. 

in vacuo, 126. 

siphon, 135. 

sponge cup, 138. 
Fractional distillation, 170. 
Frankford Exhibition, 284. 
Franklin, 86. 228. 

Benjamin, portrait of, 86. 
Freezing mixtures, 197. 
Frost, 172. 176. 
Furnace, 181, 184. 
Furness. Horace Howard, 373. 
Fusing by electricity, 151. 
Fusing point, affected by alloys, 
166. 

affected by pressure, 165. 
Fusion, 164. 

laws of, 164. 

of sulphur, 164. 

Galileo, 106. 
Galvanometer, 255. 
- Gang," 251. 
Gases, 3, 152. 

behavior of, 105 

expansion of. 200. 

relation of volume to pressure, 
112. 

and vapors, 168. 
Gay-Lussac, 162. 

G, determination of, by the pendu- 
lum, 62. 

value of, 55. 
Glottis, 369. 

Good reflectors invisible, 314. 
" Goose pimples," 204. 
Grain. 25. 
Gravitation. 37, 54. 
Gravity cell, 244. 
Great Britain, 205. 



Guarnerius, 359. 
Guericke, 106, 122. 
Gulf Stream, 205. 

Hail, 173. 

Half tones of sound, 362. 
Halos, 311. 
Handel, 367. 
Hardness, 16. 
Harmonics, 365. 
Harmony, 366. 
Hearing, 371. 
Heat, 145. 

a mode of motion, 147. 

by liquefaction of vapors, 205. 

conduction of, 178. 

convection of, 182. 

effects of, 152. 

from electricity, 247. 

from light rays, 339. 

from rain or snow, 205. 

from solutions, 205. 

from the sun, 185. 

in battery cell, 248. 

measurement of, 191. 

medium of exchange, 148. 

Newton's ideas of, 146. 

of combustion, 151. 

of earth, 150. 

of foods, 151. 

of rusting, 151. 

of the sun, 149, 150. 

produced by chemical action, 
150. 

produced by electricity, 151. 

produced by friction, 148. 

produced by percussion, 148. 

produced by pressure, 149. 

producing electric current, 284. 

quantity of, 191. 

rays, 339. 

relation to light, 187. 



382 



PHYSICS 



Heat, theory of, 153. 

transference of, 178. 

waves, 290, 346. 
Heating chemical glassware, 155. 

electric cars, 151. 

of hay, grain, etc., 151. 
Helix, 251. 
Helmholtz, 147, 150. 
Helmholtz's resonators, 356. 
Hero's fountain, 136. 
Herz, Heinrich, 342. 
Herz waves, 342. 
Hiero, 103. 

Hoffman apparatus, 10. 
Horse power, 71, 282. 
" Plot-bed," 188, 339. 
Hudson River Tunnel, 124. 
Human eye, 331. 
Human voice, range of, 370. 
Humidity, 173. 
Huxley, 12. 
Huygens, 63. 
Hydraulic, 140. 
Hydraulic ram, 140. 
Hydrochloric acid, 135. 
Hydrogen, 7, 10, 20, 21, 136. 

specific gravity of, 106. 
Hydrometer, 102. 

Nicholson's, 101. 

Baume's, 102. 
Hydrostatic, 140. 

press, 119. 

Icebergs, 165. 

Iceland spar, 345. 

Illumination of clouds at sunset, 
312. 

Illumination of page of reading 
matter, 295. 

Image curved from straight ob- 
ject, 310. 

Images by refraction, 324-327. 



Images in concave mirrors, 307, 
308. 

in convex mirrors, 309. 

in plane. mirrors, 304. 

how constructed, 305. 
Inclination of magnetic needle, 

215. 
Inclined plane, 81. 
Index of refraction, 318. 

value of, 319. 
Induced currents, direction of, 273. 

strength of, 273. 
Induction, by a magnet, 271. 

by static electricity, 226, 228. 

by varying currents, 272. 

coil, 274. 

magnetic and electric, 253. 

of electric current, 270. 
Insulators, 224. 
Intervals of sound, 362. 
Inverse squares, law of, 219, 227, 

293, 352. 
Inverted images by refraction, 325. 

in concave mirrors, 308. 
Inverted tumbler of water, 138. 
Iron bridges, 155. 
Iron oxide, 209. 
Iron ships, 103. 
Isobars, 112. 

Joule, 70, 147. 
Jupiter's satellites, 291. 

Kathode, 239. 

Kelvin, 8. 

Kelvin, Lord, portrait of, 372. 

Keyboard of piano, 361. 

Kilogram, 25. 

Kilometer, 25. 

Lactometer, 102. 
La Parge, 338. 



INDEX 



383 



Land and sea breezes, 184, 195. 
Latent heat, 205. 

of solution, 196. 

of vapors, 198. 
Laws of boiling, 170. 

of Boyle, 112. 

of Charles, 161. 

of fusion, 164. 

of inverse squares, 219, 227, 293, 
352. 

Ohm's, 260. 

of reflection, 304. 

of refraction, 318. 

of vibrating strings, 358. 

Newton's, 72. 
Leclanche cell, 243. 
" Leit-motif," 364. 
Length, 25. 
Lenses, 324. 

material of, 328. 

familiar illustration, 329. 
Leslie, 202. 
Lever, 76. 
Leyden jar, 231. 
Light, its effects, 289. 

measurement of, 293. 

polarization of, 343. 

radiations change to heat, 339. 

rays, 339. 

reflection of, 304. 

refraction of, 317. 

relation to heat, 292. 

relation to temperature, 295. 

sources of, 292. 

through small apertures, 302. 

velocity of, 290. 

waves, 290, 295, 346. 
Lightning, 231. 
Lights, artificial, 292. 
Limits of sound, 372. 
Lines of magnetic force, 220. 
Liquid air, 198. 



Liquids, 2, 152. 

Liquids seek their own level, 94. 

Liter, 25. 

Loadstone, 209. 

Local action in voltaic cell, 240. 

Loudness of sound, 351. 

Luminous paints, 339. 

Machines, 74. 

Magdeburg Hemispheres, 122. 
Magnet, effect on polarized light, 
346. 

influence upon magnetic sub- 
stances, 211. 
Magnetic effects of electricity, 251. 

field, 280. 

force, lines of, 220. 

induction, 211. 

poles, 214. 

substances, 211. 
Magnetism and electricity, rela- 
tion of, 253. 
Magnetism of the earth, 214. 
Magnetite, 209, 218. 
Magneto-electric machine, 278. 
Magneto telephone, 374. 
Magnets, 209. 
Malleability, 18. 
Mariner's compass, 217. 
Mariotte, 112. 
Mass, 25, 36. 

and weight, 36. 

measurement of, 39. 
Matter, 1. 

conservation of, 28, 71. 

measurement of, 30. 

properties of, 15. 

radiant, 3. 

three states of, 2. 
Matterhorn, 176. 
Maxwell, 7, 9, 147. 
Measurements, 24, 27. 



384 



PHYSICS 



Medicine dropper, 138. 
Melody, 363. 
Mendelssohn, 308. 
Mercury, 10. 
Mercury pumps, 131. 
Metaphysics, 5. 
Meteors. 149. 
Meter, 25. 
Metric system, 25. 
Micrometer screw, 31. 
Microscope, 329. 
Microscopic sections, 203. 
Milk, density of, 121. 
Millimeter, 25. 
Mist, 172. 
Mirrors, plane, 304. 

concave, 306. 

convex, 309. 
Mixtures and compounds, 9. 
Moisture absorbs heat radiation, 

188. 
Moisture and health, 174. 
Molecular theory of magnets, 212. 
Molecule, 2, 8. 
Molecule', size of, 8. 
Moments, 66. 
Momentum, 48. 
Monochord, 357. 
Mont Blanc, 186. 
Moon, 152. 

distance of, 291, 299. 

phases of, 312. 
Moonlight, 312. 
Moon's shadow, 298. 

umbra, 298. 
Motion, 3, 4, 47, 49. 

units of, 52. 
Motions, composition of, 64. 

parallel, 67. 

parallelogram of, 65. 

resolution of, 68. 
Motor, electric, 257, 259, 284. 



Moving body, path of, 49. 
Mozart, 368. * 

portrait of, 367. 
"Muggy "day, 204. 
Music, 360. 
Musical notation, 362. 

scale, 360, 362. 

score, 363. 

Near-sightedness, 333. 

New moon, how dark part is made 

visible, 313. 
Newton, 37, 54, 146. 
Newton, Sir Isaac, portrait of, 

Frontispiece. 
Newton's laws, 72. 
Nicholson's hydrometer, 101. 
Nitrogen, 9, 10, 202. 
Non-conductors of heat, 180. 
Norwegian cooking box, 180. 

Ocean currents, 184. 
Octave, 361. 
Ohm, 261. 

Ohm, Oeorg Simon, 261. 
Ohm's law, 260. 
Open-circuit batteries, 243. 
Osmose, 21. 
Overtones, 355, 365. 
Oxygen, 9, 10, 20. 
specific gravity of, 106. 

Palestrina, 367. 
Palisades, 155. 
Pascal, 119. 
Pendulum, compound, 63. 

simple, 59. 

motion of, 61. 

seconds, 62. 
Penumbra, 298. 
" Permanent gases," 168. 
Phases of the moon, 312. 



INDEX 



385 



Phonograph, 372. 
Phosphorescence, 338. 
Photometer, Ruinford's, 294. 
Photometry, 293. 
Physical science, 1. 
Physics, 4, 5, 7, 12, 27. 
Physiological effects of electricity, 

246. 
Piano, 358. 
Pictures at focus of lens, 327. 

through a keyhole, 303. 
Piston, 128. 
Plane mirrors, 304. 
Plante, Gaston, 248. 
Polarization, in voltaic cell, 240. 

of light, 343. 

of light, applications of, 345. 

of light, affected by magnet, 346. 

rotation of plane of, 346. 
Polarized pith ball, 226. 
Polarizers, 345. 
Poles of a magnet, 210. 

of voltaic cell, 239. 
Power, 70, 74. 

Pressure, affecting fusing point, 
165. 

due to gravity, 92. 

gauge, 89. 

gauge closed, 114. 

in gases, second principle, 105. 

in liquids, first principle, 91. 

in fluids, third principle, 118. 

upward, 93. 
Principal focus. 306. 
Print upon glazed paper, 315. 
Prism, 324. 

Projectiles, patn of, 57. 
Protyle, 11. 
Pulley, 80. 
Pump, double acting, 129. 

force, 128. 

mercury, 131. 
26 



Pump, air, 130. 
Pumps, 127. 
Pyrometers, 162. 

Quality of sound, 354. 
Quicksands, 203. 

Radiant matter, 3. 
Radiation, 184. 

identity of various forms, 346. 
Radiations, 339. 
Radiometer, 189. 
Rainfall, 173. 

table of, 174. 
Rationality, 29. 
Reaction equal action, 73. 
Reading, music, 368. 
Reaumur scale, 158. 
Receiver, telephone, 277. 
Reciprocity, 73. 
Reflection, heat, 186. 

light, 304. 

miscellaneous observations on, 
311. 

sound, 356. 

total, 321. 
Refraction, affects apparent posi- 
tion of heavenly bodies, 321. 

applications of, 321. 

cause of, 319. 

enables us to see transparent and 
colorless substances, 322. 

index of, 317. 

in prisms, 324. 

laws of, 318. 

of light, 317. 
Re-enforcement of sound, 352. 
Resistance, coils, 266. 

electric, 265. 

of metals, 268. 
Resonators, Helmholtz, 356. 
Respiration, physics of, 125. 



386 



PHYSICS 



Resultant, 64. 

Robertson, 373. 

Roemer, Olaf, 290. 

Rontgen, Prof. W. C., 340. 

Rontgen rays, 340. 

Rood, Prof. Ogden, 338. 

Rotating bodies, 51. 

Rotation of plane of polarization, 

346. 
Ruhmkorff s coil, 275. 
Ruraford, Count, 147. 

Sahara, 189. 

Salt lakes, 103. 

Saturation of vapors, 172. 

Savart's wheel, 353. 

Schumann, 366. 

Science, first course in, 289. 

Screw, 83. 

Screw gauge, 31. 

Shadows, 298. 

Shunt, 276. 

Siddons, Mrs. Scott, 373. 

Silver spoon as curved mirror, 309. 

Simple microscope, 329. 

" Single-stroke " bell, 257. 

Siphon, 132. 

aspirating, 134. 

bottles, 123. 

fountain, 135. 
Siphoning gases, 135. 
Siren, 354. 
Slaking lime, 151. 
Sleet, 173. 
Snow, 173, 175. 

protects vegetation, 182, 188. 
Solidification, 177. 
Solids, 2, 152. 

evaporation of, 167. 
Sonometer, 357. 
Sound, 347. 

by sympathetic vibrations, 352. 



Sound, half tones and whole tones, 
362. 

intervals of, 362. 

limits of, 372. 

loudness of, 351. 

miscellaneous applications, 369. 

reflection of, 356. 

re-enforcement of, 352. 

sources of, 349. 

transmission of, 349. 

velocity of, 356. 

vibration ratio of, 362. 

waves, 351. 
Spark coil, 275. 
Speaking, 369. 
Specific gravity, 43, 99. 

balance, 99. 

bottle, 45. 

of gases, 44. 

of human body, 103. 

of liquids, 100. 

of liquids by balancing against 
atmospheric pressure, 139. 

of solids, 45, 99. 
Specific heat, 192. 

applications, 194. 

table of, 194. 
Spectrum, 333. 

invisible, 336. 
Spherometer, 32. 
Spottiswoode, 275. 
Staff, musical, 363. 
Stamping metals. 165. 
Stars, distance of, 292. 
Static electricity, 222. 
Steam radiators, 205. 
Steinway, 358. 
St. Elmo's fire, 234. 
Storage batteries, 248. 
Stradivarius, 359. 
Strength of induced currents, 273. 
Sublimation, 168. 



INDEX 



387 



Sulphate of quinine. 339. 
Sulphur, fusion of, 164. 

plastic, 164. 
Sun, 152. 
Sun and moon, relative size and 

distance, 297, 299. 
Sun, distance of, 150, 291, 299. 
" Sun drawing water," 311. 
Sunset clouds, 312. 
Surveying, 33. 
Sympathetic vibrations, 359. 

Table of boiling points, 170. 

conductivity, 179. 

conductors and insulators of 
electricity, 225. 

densities, 42. 

electro-chemical series, 240. 

elements, 12. 

lineal coefficient of expansion, 
154. 

magnetic declination, inclina- 
tion, and intensity, 216. 

melting points, 165. 

rainfall, 174. 

resistance of metals, 268. 

specific heats, 194. 

tangents, 263. 
Tait. 12, 147. 
Tangent, 262. 

galvanometer, 262. 
Telegraph sounder, 255. 
Telegraph wires, 256. 
Telegraphy, wireless, 342. 
Telephone. 276. 373. 
Telescope, 330. 
Temperature, '161. 

and color, 3o9. 

at various elevations, 200. 

of birds. 163. 

of the human body, 163. 

range of, 163. 



Temperature, relation to animal 
and vegetable life, 163. 

relation to light, 295. 
Tension and pressure, relation of, 

122. 
Tesla, 292. 

Thermal effects of electricity, 247. 
Thermodynamics, 148. 
Thermo-electric currents, 284. 
Thermometer, air, 162. 

Draper's, 160. 

for high temperature, 162. 

maximum and minimum, 160. 

mercury, 157. 

alcohol, 157. 

metal, 154. 

self-recording, 160. 

standardized in steam rather 
than water, 171. 

used to determine altitude, 172. 

wet and dry bulb, 173. 
Thermopile, 285. 
Third principle of fluid pressure, 

118. 
Thompson, Benjamin, 147. 
Thomson, Sir William, 149. 

portrait of, 372. 
Tiffany, 338. 
Timbre of sound, 354. 
Time, 25. 
Time-keeping, 62. 
Tone color, 354. 
Torricelli, 107. 
Total reflection, 321. 
Tourmaline crystals, 345. 
Trade winds, 184. 
Transformers, 277. 
Transmission of pressure in fluids, 

117. 
Transmitter, telephone, 276. 
Transparent objects invisible, 314. 
Transverse vibrations, 343. 



388 



PHYSICS 



Trap rock, 155. 
Twilight, 316. 
Tyndall, 147, 175, 186. 
Tyndall, John, portrait of, 187. 
Type metal, 165. 
Typical cells, 241. 

Umbra, 298. 
Units, 2, 24. 

Vacuum pans, 167. 
Vapor in atmosphere, 172. 
Vaporization, 166. 
Vapors, 168. 

saturated, 168. 
Vapor tension, 172. 
Variations in earth's magnetism, 

217. 
Velocity, 48. 

of sound, 356. 
Ventilation, 183, 184. 
Venus, crescent-shaped, 314. 
Vernier, 32. 

Vibration ratios of sound, 362. 
Vibrations of strings, 357. 
Vibrations, transverse, 343. 
Violin, 359. 
Violoncello, 359. 
Virtual velocities, 75. 
Viscosity, 19. 
Visual angle, 296. 

of sun and moon, 297, 299. 
Vocal cords, 369. 
Volt, 237, 261. 
Volta, 237, 261. 



Voltaic cell, 238. 
Voltmeter, 264. 
Volume of stone, 34. 
Von Helmholtz, 355. 

Wagner, 364. 

Ward, Prof. R. De C, 174. 
Water as a reflector, 315. 
Water barometer, 138. 

bath, 166, 204. 

exhaust, 131. 

jars of the East, 201. 

life preserved by ice, 157. 

maximum density of, 156. 

wheels, 140. 
Watt, 70, 71, 282. 
Wave lengths, 339, 340, 346. 
Weather Bureau : 

map, 111. 

report, 112. 
Weber, 295. 
Wedge, 83. 
Weighing, 39. 
Weight, 38. 

Weight of mercury, 35. 
Welding metals by electricity, 

151. 
Wheatstone bridge, 265. 
Wheel and axle, 79. 
Windmills, 140. 
Wireless telegraphy, 342. 
Wollaston's cryophorus, 203. 
Work, 70, 74. 

X-rays, 340. 



THE END 



